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Available in 26 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-26" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">26 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Predikaatlogika" title="Predikaatlogika – Afrikaans" lang="af" hreflang="af" data-title="Predikaatlogika" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/L%C3%B2gica_de_predicats" title="Lògica de predicats – Catalan" lang="ca" hreflang="ca" data-title="Lògica de predicats" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Predik%C3%A1tov%C3%A1_logika" title="Predikátová logika – Czech" lang="cs" hreflang="cs" data-title="Predikátová logika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Pr%C3%A6dikatslogik" title="Prædikatslogik – Danish" lang="da" hreflang="da" data-title="Prædikatslogik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Pr%C3%A4dikatenlogik" title="Prädikatenlogik – German" lang="de" hreflang="de" data-title="Prädikatenlogik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Predikaatloogika" title="Predikaatloogika – Estonian" lang="et" hreflang="et" data-title="Predikaatloogika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CF%84%CE%B7%CE%B3%CE%BF%CF%81%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AE_%CE%BB%CE%BF%CE%B3%CE%B9%CE%BA%CE%AE" title="Κατηγορηματική λογική – Greek" lang="el" hreflang="el" data-title="Κατηγορηματική λογική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Predicate_logic" title="Predicate logic – English" lang="en" hreflang="en" data-title="Predicate logic" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Predikata_logiko" title="Predikata logiko – Esperanto" lang="eo" hreflang="eo" data-title="Predikata logiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8_%D9%85%D8%AD%D9%85%D9%88%D9%84%D8%A7%D8%AA" title="حساب محمولات – Persian" lang="fa" hreflang="fa" data-title="حساب محمولات" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%A0%EC%96%B4_%EB%85%BC%EB%A6%AC" title="술어 논리 – Korean" lang="ko" hreflang="ko" data-title="술어 논리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%97%D7%A9%D7%99%D7%91_%D7%94%D7%A4%D7%A8%D7%93%D7%99%D7%A7%D7%98%D7%99%D7%9D" title="תחשיב הפרדיקטים – Hebrew" lang="he" hreflang="he" data-title="תחשיב הפרדיקטים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%B4%D0%B8%D0%BA%D0%B0%D1%82%D1%82%D1%8B%D2%9B_%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0" title="Предикаттық логика – Kazakh" lang="kk" hreflang="kk" data-title="Предикаттық логика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Predikat%C5%B3_logika" title="Predikatų logika – Lithuanian" lang="lt" hreflang="lt" data-title="Predikatų logika" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Els%C5%91rend%C5%B1_logika" title="Elsőrendű logika – Hungarian" lang="hu" hreflang="hu" data-title="Elsőrendű logika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%B4%D0%B8%D0%BA%D0%B0%D1%82%D0%BD%D0%B0_%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0" title="Предикатна логика – Macedonian" lang="mk" hreflang="mk" data-title="Предикатна логика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Predicatenlogica" title="Predicatenlogica – Dutch" lang="nl" hreflang="nl" data-title="Predicatenlogica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%BF%B0%E8%AA%9E%E8%AB%96%E7%90%86" title="述語論理 – Japanese" lang="ja" hreflang="ja" data-title="述語論理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Predikatlogikk" title="Predikatlogikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Predikatlogikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/L%C3%B3gica_de_predicados" title="Lógica de predicados – Portuguese" lang="pt" hreflang="pt" data-title="Lógica de predicados" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a href="https://ru.wikipedia.org/wiki/%D0%98%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BF%D1%80%D0%B5%D0%B4%D0%B8%D0%BA%D0%B0%D1%82%D0%BE%D0%B2" title="Исчисление предикатов – Russian" lang="ru" hreflang="ru" data-title="Исчисление предикатов" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Predik%C3%A1tov%C3%A1_logika" title="Predikátová logika – Slovak" lang="sk" hreflang="sk" data-title="Predikátová logika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Predikaattilogiikka" title="Predikaattilogiikka – Finnish" lang="fi" hreflang="fi" data-title="Predikaattilogiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Predikatlogik" title="Predikatlogik – Swedish" lang="sv" hreflang="sv" data-title="Predikatlogik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D1%96%D0%BA%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B8%D0%BA%D0%B0%D1%82%D1%96%D0%B2" title="Логіка предикатів – Ukrainian" lang="uk" hreflang="uk" data-title="Логіка предикатів" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B0%93%E8%AF%8D%E9%80%BB%E8%BE%91" title="谓词逻辑 – 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Merge-arrows.svg/75px-Merge-arrows.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Merge-arrows.svg/100px-Merge-arrows.svg.png 2x" data-file-width="50" data-file-height="20" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">It has been suggested that this article be <a href="/wiki/Wikipedia:Merging_and_moving_pages" title="Wikipedia:Merging and moving pages">merged</a> with <i><a href="/wiki/First_order_logic" title="First order logic">First order logic</a></i>. (<a href="/w/index.php?title=Talk:Predicate_logic&action=edit&redlink=1" class="new" title="Talk:Predicate logic (not yet started)">Discuss</a>)</div></td></tr></tbody></table> <p>In logic and philosophy, <b>predicate logic</b> is a system of mathematical <a href="/wiki/Logic" title="Logic">logic</a>. It uses <a href="/w/index.php?title=Predicate&action=edit&redlink=1" class="new" title="Predicate (not yet started)">predicates</a> to express the state of certain things, which are "incomplete <a href="/wiki/Proposition" title="Proposition">propositions</a>" with a placeholder for objects or subjects that must be inserted in order to obtain a valid proposition. </p><p>The term "predicate logic" has 2 meanings: </p><p>1. <a href="/wiki/First_order_logic" title="First order logic">First order logic</a> (more often used); 2. Any logic(i.e. any formal logical system) that uses predicates. </p><p>Any predicate logic is different from <a href="/wiki/Propositional_logic" title="Propositional logic">propositional logic</a>, in part because it has the concept of <i><a href="/wiki/Logical_quantifier" title="Logical quantifier">quantifiers</a></i>. A quantifier is used in conjunction with a variable (say <i>x</i>) in order to talk about a general instance of x, and in doing so, this allows predicate logic to make statements about quantity. </p><p>The best-known quantifiers are the <i>existential quantifier</i>, represented by ∃, and the <i><a href="/wiki/Universal_quantifier" title="Universal quantifier">universal quantifier</a></i>, represented by ∀.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The existential quantifier is used to express statements of the form "there exists", and is true precisely when there is at least one mathematical object from the <a href="/wiki/Universe_of_discourse" title="Universe of discourse">universe of discourse</a> that matches the predicate or formula. On the other hand, the universal quantifier is used to express statements of the form "for all", and is true precisely when all possible mathematical objects of the universe of discourse match the specified predicate or formula.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>In the notation of predicate logic, quantifiers directly precede (and thus introduce) variable names, which are then followed by other quantifiers or mathematical expressions, where the said variables are found. For example. one can use the expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x\forall yLyx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mi mathvariant="normal">∀</mi> <mi>y</mi> <mi>L</mi> <mi>y</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x\forall yLyx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eb6c5067e35bf3be003ce9a514dbc54deac9456" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.138ex; height:2.509ex;" alt="{\displaystyle \exists x\forall yLyx}"></span> to mean "there is a person <i>x</i> such that for all persons <i>y</i>, y likes x" ("everyone is liked by someone.").<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Predicate_logic&veaction=edit&section=1" title="Change section: Examples" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Predicate_logic&action=edit&section=1" title="Edit section's source code: Examples"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists c\ ({\text{Cat}}(c)\land {\text{isBlack}}(c)\land \exists d\ ({\text{Dog}}(d)\land {\text{likes}}(c,d)))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>c</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cat</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>isBlack</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi mathvariant="normal">∃</mi> <mi>d</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Dog</mtext> </mrow> <mo stretchy="false">(</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>likes</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo>,</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists c\ ({\text{Cat}}(c)\land {\text{isBlack}}(c)\land \exists d\ ({\text{Dog}}(d)\land {\text{likes}}(c,d)))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/048c9d3030fc27ada1fa0751f616b88f860ef704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:50.652ex; height:2.843ex;" alt="{\displaystyle \exists c\ ({\text{Cat}}(c)\land {\text{isBlack}}(c)\land \exists d\ ({\text{Dog}}(d)\land {\text{likes}}(c,d)))}"></span> </p><p>can be read as: "There is at least one cat which is black, and which likes (one or more) dogs." </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \forall c\ ({\text{Cat}}(c)\to \forall d\ ({\text{Dog}}(d)\to \neg {\text{likes}}(c,d)))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi mathvariant="normal">∀</mi> <mi>c</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cat</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi mathvariant="normal">∀</mi> <mi>d</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Dog</mtext> </mrow> <mo stretchy="false">(</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi mathvariant="normal">¬</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>likes</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo>,</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \forall c\ ({\text{Cat}}(c)\to \forall d\ ({\text{Dog}}(d)\to \neg {\text{likes}}(c,d)))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41db3c234ea68633032df49521382d62e76a3f30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.139ex; height:2.843ex;" alt="{\displaystyle \neg \forall c\ ({\text{Cat}}(c)\to \forall d\ ({\text{Dog}}(d)\to \neg {\text{likes}}(c,d)))}"></span> </p><p>can be read as: "It is not true that every cat doesn't like any dog." </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \exists c\ ({\text{Cat}}(c)\land {\text{Dog}}(c))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi mathvariant="normal">∃</mi> <mi>c</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cat</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Dog</mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \exists c\ ({\text{Cat}}(c)\land {\text{Dog}}(c))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86c3562c3bf972b895d8ae024e302bec2c244818" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.3ex; height:2.843ex;" alt="{\displaystyle \neg \exists c\ ({\text{Cat}}(c)\land {\text{Dog}}(c))}"></span> </p><p>can be read as: "There does not exist a cat which is also a dog." </p> <div class="mw-heading mw-heading2"><h2 id="Related_pages">Related pages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Predicate_logic&veaction=edit&section=2" title="Change section: Related pages" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Predicate_logic&action=edit&section=2" title="Edit section's source code: Related pages"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/First_order_logic" title="First order logic">First order logic</a></li> <li><a href="/wiki/Fuzzy_logic" title="Fuzzy logic">Fuzzy logic</a></li> <li><a href="/wiki/Rule_of_inference" title="Rule of inference">Rule of inference</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Predicate_logic&veaction=edit&section=3" title="Change section: References" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Predicate_logic&action=edit&section=3" title="Edit section's source code: References"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r9724332">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathvault.ca/hub/higher-math/math-symbols/set-theory-symbols/">"Comprehensive List of Set Theory Symbols"</a>. <i>Math Vault</i>. 2020-04-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Math+Vault&rft.atitle=Comprehensive+List+of+Set+Theory+Symbols&rft.date=2020-04-11&rft_id=https%3A%2F%2Fmathvault.ca%2Fhub%2Fhigher-math%2Fmath-symbols%2Fset-theory-symbols%2F&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3APredicate+logic" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.geeksforgeeks.org/mathematic-logic-predicates-quantifiers/">"Mathematics | Predicates and Quantifiers | Set 1"</a>. <i>GeeksforGeeks</i>. 2015-06-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GeeksforGeeks&rft.atitle=Mathematics+%7C+Predicates+and+Quantifiers+%7C+Set+1&rft.date=2015-06-24&rft_id=https%3A%2F%2Fwww.geeksforgeeks.org%2Fmathematic-logic-predicates-quantifiers%2F&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3APredicate+logic" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://brilliant.org/wiki/predicate-logic/">"Predicate Logic | Brilliant Math & Science Wiki"</a>. <i>brilliant.org</i><span class="reference-accessdate">. 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class="new" title="Template talk:Mathematical logic (not yet started)"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://simple.wikipedia.org/w/index.php?title=Template:Mathematical_logic&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Mathematical_logic" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a> <ul><li><a href="/w/index.php?title=List_of_axioms&action=edit&redlink=1" class="new" title="List of axioms (not yet started)">list</a></li></ul></li> <li><a href="/wiki/Cardinality" title="Cardinality">Cardinality</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Lemma_(mathematics)" title="Lemma (mathematics)">Lemma</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/w/index.php?title=First-order_logic&action=edit&redlink=1" class="new" title="First-order logic (not yet started)">First-order logic</a></li> <li><a href="/w/index.php?title=Formal_proof&action=edit&redlink=1" class="new" title="Formal proof (not yet started)">Formal proof</a></li> <li><a href="/w/index.php?title=Formal_semantics_(logic)&action=edit&redlink=1" class="new" title="Formal semantics (logic) (not yet started)">Formal semantics</a></li> <li><a href="/w/index.php?title=Foundations_of_mathematics&action=edit&redlink=1" class="new" title="Foundations of mathematics (not yet started)">Foundations of mathematics</a></li> <li><a href="/w/index.php?title=Logical_consequence&action=edit&redlink=1" class="new" title="Logical consequence (not yet started)">Logical consequence</a></li> <li><a href="/w/index.php?title=Structure_(mathematical_logic)&action=edit&redlink=1" class="new" title="Structure (mathematical logic) (not yet started)">Model</a></li> <li><a href="/w/index.php?title=Theory_(mathematical_logic)&action=edit&redlink=1" class="new" title="Theory (mathematical logic) (not yet started)">Theory</a></li> <li><a href="/w/index.php?title=Type_theory&action=edit&redlink=1" class="new" title="Type theory (not yet started)">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems (<a href="/w/index.php?title=Category:Theorems_in_the_foundations_of_mathematics&action=edit&redlink=1" class="new" title="Category:Theorems in the foundations of mathematics (not yet started)">list</a>)<br /> & <a href="/w/index.php?title=Paradoxes_of_set_theory&action=edit&redlink=1" class="new" title="Paradoxes of set theory (not yet started)">Paradoxes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/w/index.php?title=G%C3%B6del%27s_completeness_theorem&action=edit&redlink=1" class="new" title="Gödel's completeness theorem (not yet started)">Gödel's completeness</a> and <a href="/wiki/G%C3%B6del%27s_incompleteness_theorems" title="Gödel's incompleteness theorems">incompleteness theorems</a></span></li> <li><a href="/wiki/Banach%E2%80%93Tarski_paradox" title="Banach–Tarski paradox">Banach–Tarski paradox</a></li> <li><span class="nowrap">Cantor's <a href="/wiki/Cantor%27s_theorem" title="Cantor's theorem">theorem,</a> <a href="/w/index.php?title=Cantor%27s_paradox&action=edit&redlink=1" class="new" title="Cantor's paradox (not yet started)">paradox</a> and <a href="/wiki/Cantor%27s_diagonal_argument" title="Cantor's diagonal argument">diagonal argument</a></span></li> <li><a href="/wiki/Halting_problem" title="Halting problem">Halting problem</a></li> <li><a href="/wiki/Russell%27s_paradox" title="Russell's paradox">Russell's paradox</a></li> <li><a href="/w/index.php?title=Tarski%27s_undefinability_theorem&action=edit&redlink=1" class="new" title="Tarski's undefinability theorem (not yet started)">Tarski's undefinability</a></li> <li><a href="/w/index.php?title=Compactness_theorem&action=edit&redlink=1" class="new" title="Compactness theorem (not yet started)">Compactness</a></li> <li><a href="/w/index.php?title=Lindstr%C3%B6m%27s_theorem&action=edit&redlink=1" class="new" title="Lindström's theorem (not yet started)">Lindström's</a></li> <li><a href="/w/index.php?title=L%C3%B6wenheim%E2%80%93Skolem_theorem&action=edit&redlink=1" class="new" title="Löwenheim–Skolem theorem (not yet started)">Löwenheim–Skolem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Logic" title="Logic">Logics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Traditional" scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Term_logic&action=edit&redlink=1" class="new" title="Term logic (not yet started)">Traditional</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Tautology_(logic)" title="Tautology (logic)">Tautology</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Logical_equivalence" title="Logical equivalence">Logical equivalence</a></li> <li><a href="/wiki/Consistency" class="mw-disambig" title="Consistency">Consistency</a> <ul><li><a href="/w/index.php?title=Equiconsistency&action=edit&redlink=1" class="new" title="Equiconsistency (not yet started)">Equiconsistency</a></li></ul></li> <li><a href="/wiki/Argument" title="Argument">Argument</a></li> <li><a href="/wiki/Syllogism" title="Syllogism">Syllogism</a></li> <li><a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagram</a></li> <li><a href="/w/index.php?title=Classical_logic&action=edit&redlink=1" class="new" title="Classical logic (not yet started)">Classical logic</a></li> <li><a href="/w/index.php?title=Logical_truth&action=edit&redlink=1" class="new" title="Logical truth (not yet started)">Logical truth</a></li> <li><a href="/w/index.php?title=Soundness&action=edit&redlink=1" class="new" title="Soundness (not yet started)">Soundness</a></li> <li><a href="/w/index.php?title=Validity_(logic)&action=edit&redlink=1" class="new" title="Validity (logic) (not yet started)">Validity</a></li> <li><a href="/w/index.php?title=Square_of_opposition&action=edit&redlink=1" class="new" title="Square of opposition (not yet started)">Square of opposition</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Propositional_calculus" class="mw-redirect" title="Propositional calculus">Propositional</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Propositional_calculus" class="mw-redirect" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Truth_table" title="Truth table">Truth tables</a></li> <li><a href="/w/index.php?title=Boolean_function&action=edit&redlink=1" class="new" title="Boolean function (not yet started)">Boolean functions</a></li> <li><a href="/w/index.php?title=Logical_connective&action=edit&redlink=1" class="new" title="Logical connective (not yet started)">Logical connectives</a></li> <li><a href="/w/index.php?title=Propositional_formula&action=edit&redlink=1" class="new" title="Propositional formula (not yet started)">Propositional formula</a></li> <li><a href="/wiki/Many-valued_logic" class="mw-redirect" title="Many-valued logic">Many-valued logic</a> <ul><li><a href="/w/index.php?title=Three-valued_logic&action=edit&redlink=1" class="new" title="Three-valued logic (not yet started)">3</a></li> <li><a href="/w/index.php?title=Finite-valued_logic&action=edit&redlink=1" class="new" title="Finite-valued logic (not yet started)">Finite</a></li> <li><a href="/w/index.php?title=Infinite-valued_logic&action=edit&redlink=1" class="new" title="Infinite-valued logic (not yet started)">∞</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Predicate</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=First-order_logic&action=edit&redlink=1" class="new" title="First-order logic (not yet started)">First-order</a> <ul><li><a href="/w/index.php?title=List_of_first-order_theories&action=edit&redlink=1" class="new" title="List of first-order theories (not yet started)"><span style="font-size:85%;">list</span></a></li></ul></li> <li><a href="/w/index.php?title=Second-order_logic&action=edit&redlink=1" class="new" title="Second-order logic (not yet started)">Second-order</a> <ul><li><a href="/w/index.php?title=Monadic_second-order_logic&action=edit&redlink=1" class="new" title="Monadic second-order logic (not yet started)">Monadic</a></li></ul></li> <li><a href="/w/index.php?title=Higher-order_logic&action=edit&redlink=1" class="new" title="Higher-order logic (not yet started)">Higher-order</a></li> <li><a href="/w/index.php?title=Free_logic&action=edit&redlink=1" class="new" title="Free logic (not yet started)">Free</a></li> <li><a href="/w/index.php?title=Quantifier_(logic)&action=edit&redlink=1" class="new" title="Quantifier (logic) (not yet started)">Quantifiers</a></li> <li><a href="/w/index.php?title=Predicate_(mathematical_logic)&action=edit&redlink=1" class="new" title="Predicate (mathematical logic) (not yet started)">Predicate</a></li> <li><a href="/w/index.php?title=Monadic_predicate_calculus&action=edit&redlink=1" class="new" title="Monadic predicate calculus (not yet started)">Monadic predicate calculus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Set_theory" title="Set theory">Set theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Set</a> <ul><li><a href="/w/index.php?title=Hereditary_set&action=edit&redlink=1" class="new" title="Hereditary set (not yet started)">Hereditary</a></li></ul></li> <li>(<a href="/w/index.php?title=Urelement&action=edit&redlink=1" class="new" title="Urelement (not yet started)">Ur-</a>)<a href="/wiki/Element_(mathematics)" class="mw-redirect" title="Element (mathematics)">Element</a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a></li> <li><a href="/wiki/Relation_(mathematics)" title="Relation (mathematics)">Relation</a> <ul><li><a href="/wiki/Equivalence_relation" title="Equivalence relation">Equivalence</a></li> <li><a href="/w/index.php?title=Partition_of_a_set&action=edit&redlink=1" class="new" title="Partition of a set (not yet started)">Partition</a></li></ul></li> <li>Set operations: <ul><li><a href="/wiki/Intersection_(set_theory)" class="mw-redirect" title="Intersection (set theory)">Intersection</a></li> <li><a href="/wiki/Union_(set_theory)" class="mw-redirect" title="Union (set theory)">Union</a></li> <li><a href="/wiki/Complement_(set_theory)" class="mw-redirect" title="Complement (set theory)">Complement</a></li> <li><a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a></li> <li><a href="/wiki/Power_set" title="Power set">Power set</a></li> <li><a href="/w/index.php?title=List_of_set_identities_and_relations&action=edit&redlink=1" class="new" title="List of set identities and relations (not yet started)">Identities</a></li></ul></li> <li><a href="/w/index.php?title=Class_(set_theory)&action=edit&redlink=1" class="new" title="Class (set theory) (not yet started)">Class</a></li> <li><a href="/w/index.php?title=Extensionality&action=edit&redlink=1" class="new" title="Extensionality (not yet started)">Extensionality</a></li> <li><a href="/w/index.php?title=Forcing_(mathematics)&action=edit&redlink=1" class="new" title="Forcing (mathematics) (not yet started)">Forcing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Set_(mathematics)" class="mw-redirect" title="Set (mathematics)">Sets</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Countable_set" title="Countable set">Countable</a></li> <li><a href="/wiki/Uncountable_set" title="Uncountable set">Uncountable</a></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty</a></li> <li><a href="/w/index.php?title=Inhabited_set&action=edit&redlink=1" class="new" title="Inhabited set (not yet started)">Inhabited</a></li> <li><a href="/w/index.php?title=Singleton_(mathematics)&action=edit&redlink=1" class="new" title="Singleton (mathematics) (not yet started)">Singleton</a></li> <li><a href="/wiki/Finite_set" title="Finite set">Finite</a></li> <li><a href="/w/index.php?title=Infinite_set&action=edit&redlink=1" class="new" title="Infinite set (not yet started)">Infinite</a></li> <li><a href="/w/index.php?title=Transitive_set&action=edit&redlink=1" class="new" title="Transitive set (not yet started)">Transitive</a></li> <li><a href="/w/index.php?title=Ultrafilter_(set_theory)&action=edit&redlink=1" class="new" title="Ultrafilter (set theory) (not yet started)">Ultrafilter</a></li> <li><a href="/w/index.php?title=Recursive_set&action=edit&redlink=1" class="new" title="Recursive set (not yet started)">Recursive</a></li> <li><a href="/w/index.php?title=Fuzzy_set&action=edit&redlink=1" class="new" title="Fuzzy set (not yet started)">Fuzzy</a></li> <li><a href="/w/index.php?title=Universal_set&action=edit&redlink=1" class="new" title="Universal set (not yet started)">Universal</a></li> <li><a href="/w/index.php?title=Universe_(mathematics)&action=edit&redlink=1" class="new" title="Universe (mathematics) (not yet started)">Universe</a> <ul><li><a href="/w/index.php?title=Constructible_universe&action=edit&redlink=1" class="new" title="Constructible universe (not yet started)">Constructible</a></li> <li><a href="/w/index.php?title=Grothendieck_universe&action=edit&redlink=1" class="new" title="Grothendieck universe (not yet started)">Grothendieck</a></li> <li><a href="/w/index.php?title=Von_Neumann_universe&action=edit&redlink=1" class="new" title="Von Neumann universe (not yet started)">Von Neumann</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Map_(mathematics)&action=edit&redlink=1" class="new" title="Map (mathematics) (not yet started)">Maps</a> & <a href="/wiki/Cardinality" title="Cardinality">Cardinality</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">Function</a>/<a href="/w/index.php?title=Map_(mathematics)&action=edit&redlink=1" class="new" title="Map (mathematics) (not yet started)">Map</a> <ul><li><a href="/w/index.php?title=Domain_of_a_function&action=edit&redlink=1" class="new" title="Domain of a function (not yet started)">Domain</a></li> <li><a href="/wiki/Codomain" class="mw-redirect" title="Codomain">Codomain</a></li> <li><a href="/w/index.php?title=Image_(mathematics)&action=edit&redlink=1" class="new" title="Image (mathematics) (not yet started)">Image</a></li></ul></li> <li><a href="/wiki/Injective_function" title="Injective function">In</a>/<a href="/wiki/Surjective_function" title="Surjective function">Sur</a>/<a href="/wiki/Bijection" class="mw-redirect" title="Bijection">Bi</a>-jection</li> <li><a href="/w/index.php?title=Schr%C3%B6der%E2%80%93Bernstein_theorem&action=edit&redlink=1" class="new" title="Schröder–Bernstein theorem (not yet started)">Schröder–Bernstein theorem</a></li> <li><a href="/wiki/Isomorphism" title="Isomorphism">Isomorphism</a></li> <li><a href="/wiki/G%C3%B6del_numbering" class="mw-redirect" title="Gödel numbering">Gödel numbering</a></li> <li><a href="/w/index.php?title=Enumeration&action=edit&redlink=1" class="new" title="Enumeration (not yet started)">Enumeration</a></li> <li><a href="/w/index.php?title=Large_cardinal&action=edit&redlink=1" class="new" title="Large cardinal (not yet started)">Large cardinal</a> <ul><li><a href="/w/index.php?title=Inaccessible_cardinal&action=edit&redlink=1" class="new" title="Inaccessible cardinal (not yet started)">Inaccessible</a></li></ul></li> <li><a href="/w/index.php?title=Aleph_number&action=edit&redlink=1" class="new" title="Aleph number (not yet started)">Aleph number</a></li> <li><a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">Operation</a> <ul><li><a href="/wiki/Binary_operation" title="Binary operation">Binary</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Set theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Zermelo–Fraenkel</a> <ul><li><a href="/wiki/Axiom_of_choice" title="Axiom of choice">Axiom of choice</a></li> <li><a href="/wiki/Continuum_hypothesis" title="Continuum hypothesis">Continuum hypothesis</a></li></ul></li> <li><a href="/w/index.php?title=General_set_theory&action=edit&redlink=1" class="new" title="General set theory (not yet started)">General</a></li> <li><a href="/w/index.php?title=Kripke%E2%80%93Platek_set_theory&action=edit&redlink=1" class="new" title="Kripke–Platek set theory (not yet started)">Kripke–Platek</a></li> <li><a href="/w/index.php?title=Morse%E2%80%93Kelley_set_theory&action=edit&redlink=1" class="new" title="Morse–Kelley set theory (not yet started)">Morse–Kelley</a></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive</a></li> <li><a href="/w/index.php?title=New_Foundations&action=edit&redlink=1" class="new" title="New Foundations (not yet started)">New Foundations</a></li> <li><a href="/w/index.php?title=Tarski%E2%80%93Grothendieck_set_theory&action=edit&redlink=1" class="new" title="Tarski–Grothendieck set theory (not yet started)">Tarski–Grothendieck</a></li> <li><a href="/w/index.php?title=Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory&action=edit&redlink=1" class="new" title="Von Neumann–Bernays–Gödel set theory (not yet started)">Von Neumann–Bernays–Gödel</a></li> <li><a href="/w/index.php?title=Ackermann_set_theory&action=edit&redlink=1" class="new" title="Ackermann set theory (not yet started)">Ackermann</a></li> <li><a href="/w/index.php?title=Constructive_set_theory&action=edit&redlink=1" class="new" title="Constructive set theory (not yet started)">Constructive</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Formal_system&action=edit&redlink=1" class="new" title="Formal system (not yet started)">Formal systems</a> (<a href="/w/index.php?title=List_of_formal_systems&action=edit&redlink=1" class="new" title="List of formal systems (not yet started)"><span style="font-size:85%;">list</span></a>),<br /><a href="/wiki/Formal_language" title="Formal language">Language</a> & <a href="/w/index.php?title=Syntax_(logic)&action=edit&redlink=1" class="new" title="Syntax (logic) (not yet started)">Syntax</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Alphabet_(formal_languages)&action=edit&redlink=1" class="new" title="Alphabet (formal languages) (not yet started)">Alphabet</a></li> <li><a href="/wiki/Arity" title="Arity">Arity</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata</a></li> <li><a href="/w/index.php?title=Axiom_schema&action=edit&redlink=1" class="new" title="Axiom schema (not yet started)">Axiom schema</a></li> <li><a href="/w/index.php?title=Expression_(mathematics)&action=edit&redlink=1" class="new" title="Expression (mathematics) (not yet started)">Expression</a> <ul><li><a href="/w/index.php?title=Ground_expression&action=edit&redlink=1" class="new" title="Ground expression (not yet started)">Ground</a></li></ul></li> <li><a href="/w/index.php?title=Extension_by_new_constant_and_function_names&action=edit&redlink=1" class="new" title="Extension by new constant and function names (not yet started)">Extension</a> <ul><li><a href="/w/index.php?title=Extension_by_definitions&action=edit&redlink=1" class="new" title="Extension by definitions (not yet started)">by definition</a></li> <li><a href="/w/index.php?title=Conservative_extension&action=edit&redlink=1" class="new" title="Conservative extension (not yet started)">Conservative</a></li></ul></li> <li><a href="/w/index.php?title=Finitary_relation&action=edit&redlink=1" class="new" title="Finitary relation (not yet started)">Relation</a></li> <li><a href="/w/index.php?title=Formation_rule&action=edit&redlink=1" class="new" title="Formation rule (not yet started)">Formation rule</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Grammar</a></li> <li><a href="/w/index.php?title=Well-formed_formula&action=edit&redlink=1" class="new" title="Well-formed formula (not yet started)">Formula</a> <ul><li><a href="/w/index.php?title=Atomic_formula&action=edit&redlink=1" class="new" title="Atomic formula (not yet started)">Atomic</a></li> <li><a href="/w/index.php?title=Sentence_(mathematical_logic)&action=edit&redlink=1" class="new" title="Sentence (mathematical logic) (not yet started)">Closed</a></li> <li><a href="/w/index.php?title=Ground_formula&action=edit&redlink=1" class="new" title="Ground formula (not yet started)">Ground</a></li> <li><a href="/w/index.php?title=Open_formula&action=edit&redlink=1" class="new" title="Open formula (not yet started)">Open</a></li></ul></li> <li><a href="/w/index.php?title=Free_variables_and_bound_variables&action=edit&redlink=1" class="new" title="Free variables and bound variables (not yet started)">Free/bound variable</a></li> <li><a href="/wiki/Formal_language" title="Formal language">Language</a></li> <li><a href="/w/index.php?title=Metalanguage&action=edit&redlink=1" class="new" title="Metalanguage (not yet started)">Metalanguage</a></li> <li><a href="/w/index.php?title=Logical_connective&action=edit&redlink=1" class="new" title="Logical connective (not yet started)">Logical connective</a> <ul><li><a href="/w/index.php?title=Negation&action=edit&redlink=1" class="new" title="Negation (not yet started)">¬</a></li> <li><a href="/wiki/Logical_disjunction" class="mw-redirect mw-disambig" title="Logical disjunction">∨</a></li> <li><a href="/wiki/Logical_conjunction" title="Logical conjunction">∧</a></li> <li><a href="/w/index.php?title=Material_conditional&action=edit&redlink=1" class="new" title="Material conditional (not yet started)">→</a></li> <li><a href="/w/index.php?title=Logical_biconditional&action=edit&redlink=1" class="new" title="Logical biconditional (not yet started)">↔</a></li> <li><a href="/w/index.php?title=Logical_equality&action=edit&redlink=1" class="new" title="Logical equality (not yet started)">=</a></li></ul></li> <li><a href="/w/index.php?title=Predicate_(mathematical_logic)&action=edit&redlink=1" class="new" title="Predicate (mathematical logic) (not yet started)">Predicate</a> <ul><li><a href="/w/index.php?title=Functional_predicate&action=edit&redlink=1" class="new" title="Functional predicate (not yet started)">Functional</a></li> <li><a href="/w/index.php?title=Predicate_variable&action=edit&redlink=1" class="new" title="Predicate variable (not yet started)">Variable</a></li> <li><a href="/w/index.php?title=Propositional_variable&action=edit&redlink=1" class="new" title="Propositional variable (not yet started)">Propositional variable</a></li></ul></li> <li><a href="/w/index.php?title=Formal_proof&action=edit&redlink=1" class="new" title="Formal proof (not yet started)">Proof</a></li> <li><a href="/w/index.php?title=Quantifier_(logic)&action=edit&redlink=1" class="new" title="Quantifier (logic) (not yet started)">Quantifier</a> <ul><li><a href="/w/index.php?title=Existential_quantification&action=edit&redlink=1" class="new" title="Existential quantification (not yet started)">∃</a></li> <li><a href="/w/index.php?title=Uniqueness_quantification&action=edit&redlink=1" class="new" title="Uniqueness quantification (not yet started)">!</a></li> <li><a href="/w/index.php?title=Universal_quantification&action=edit&redlink=1" class="new" title="Universal quantification (not yet started)">∀</a></li> <li><a href="/w/index.php?title=Quantifier_rank&action=edit&redlink=1" class="new" title="Quantifier rank (not yet started)">rank</a></li></ul></li> <li><a href="/w/index.php?title=Sentence_(mathematical_logic)&action=edit&redlink=1" class="new" title="Sentence (mathematical logic) (not yet started)">Sentence</a> <ul><li><a href="/w/index.php?title=Atomic_sentence&action=edit&redlink=1" class="new" title="Atomic sentence (not yet started)">Atomic</a></li> <li><a href="/w/index.php?title=Spectrum_of_a_sentence&action=edit&redlink=1" class="new" title="Spectrum of a sentence (not yet started)">Spectrum</a></li></ul></li> <li><a href="/w/index.php?title=Signature_(logic)&action=edit&redlink=1" class="new" title="Signature (logic) (not yet started)">Signature</a></li> <li><a href="/w/index.php?title=String_(formal_languages)&action=edit&redlink=1" class="new" title="String (formal languages) (not yet started)">String</a></li> <li><a href="/w/index.php?title=Substitution_(logic)&action=edit&redlink=1" class="new" title="Substitution (logic) (not yet started)">Substitution</a></li> <li><a href="/w/index.php?title=Symbol_(formal)&action=edit&redlink=1" class="new" title="Symbol (formal) (not yet started)">Symbol</a> <ul><li><a href="/w/index.php?title=Uninterpreted_function&action=edit&redlink=1" class="new" title="Uninterpreted function (not yet started)">Function</a></li> <li><a href="/w/index.php?title=Logical_constant&action=edit&redlink=1" class="new" title="Logical constant (not yet started)">Logical/Constant</a></li> <li><a href="/w/index.php?title=Non-logical_symbol&action=edit&redlink=1" class="new" title="Non-logical symbol (not yet started)">Non-logical</a></li> <li><a href="/wiki/Variable_(mathematics)" class="mw-redirect" title="Variable (mathematics)">Variable</a></li></ul></li> <li><a href="/w/index.php?title=Term_(logic)&action=edit&redlink=1" class="new" title="Term (logic) (not yet started)">Term</a></li> <li><a href="/w/index.php?title=Theory_(mathematical_logic)&action=edit&redlink=1" class="new" title="Theory (mathematical logic) (not yet started)">Theory</a> <ul><li><a href="/w/index.php?title=List_of_mathematical_theories&action=edit&redlink=1" class="new" title="List of mathematical theories (not yet started)"><span style="font-size:85%;">list</span></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="nowrap">Example <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic<br />systems</a> <span style="font-size:85%;">(<a href="/w/index.php?title=List_of_first-order_theories&action=edit&redlink=1" class="new" title="List of first-order theories (not yet started)">list</a>)</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>of <a href="/w/index.php?title=Foundations_of_geometry&action=edit&redlink=1" class="new" title="Foundations of geometry (not yet started)">geometry</a>: <ul><li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a>: <ul><li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a></li> <li><a href="/w/index.php?title=Hilbert%27s_axioms&action=edit&redlink=1" class="new" title="Hilbert's axioms (not yet started)">Hilbert's</a></li> <li><a href="/w/index.php?title=Tarski%27s_axioms&action=edit&redlink=1" class="new" title="Tarski's axioms (not yet started)">Tarski's</a></li></ul></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean</a>* of <a href="/w/index.php?title=True_arithmetic&action=edit&redlink=1" class="new" title="True arithmetic (not yet started)">arithmetic</a>:</li> <li><a href="/w/index.php?title=Peano_axioms&action=edit&redlink=1" class="new" title="Peano axioms (not yet started)">Peano</a></li> <li><a href="/w/index.php?title=Second-order_arithmetic&action=edit&redlink=1" class="new" title="Second-order arithmetic (not yet started)">second-order</a></li> <li><a href="/w/index.php?title=Elementary_function_arithmetic&action=edit&redlink=1" class="new" title="Elementary function arithmetic (not yet started)">elementary function</a></li> <li><a href="/w/index.php?title=Primitive_recursive_arithmetic&action=edit&redlink=1" class="new" title="Primitive recursive arithmetic (not yet started)">primitive recursive</a></li> <li><a href="/w/index.php?title=Robinson_arithmetic&action=edit&redlink=1" class="new" title="Robinson arithmetic (not yet started)">Robinson</a></li> <li><a href="/w/index.php?title=Skolem_arithmetic&action=edit&redlink=1" class="new" title="Skolem arithmetic (not yet started)">Skolem</a></li></ul></li> <li>of the <a href="/w/index.php?title=Construction_of_the_real_numbers&action=edit&redlink=1" class="new" title="Construction of the real numbers (not yet started)">real numbers</a> <ul><li><a href="/w/index.php?title=Tarski%27s_axiomatization_of_the_reals&action=edit&redlink=1" class="new" title="Tarski's axiomatization of the reals (not yet started)">Tarski's axiomatization</a></li></ul></li> <li>of <a href="/w/index.php?title=Axiomatization_of_Boolean_algebras&action=edit&redlink=1" class="new" title="Axiomatization of Boolean algebras (not yet started)">Boolean algebras</a> <ul><li><a href="/w/index.php?title=Boolean_algebras_canonically_defined&action=edit&redlink=1" class="new" title="Boolean algebras canonically defined (not yet started)">canonical</a></li> <li><a href="/w/index.php?title=Minimal_axioms_for_Boolean_algebra&action=edit&redlink=1" class="new" title="Minimal axioms for Boolean algebra (not yet started)">minimal axioms</a></li></ul></li></ul> <ul><li><i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Proof_theory&action=edit&redlink=1" class="new" title="Proof theory (not yet started)">Proof theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Formal_proof&action=edit&redlink=1" class="new" title="Formal proof (not yet started)">Formal proof</a></li> <li><a href="/wiki/Natural_deduction" title="Natural deduction">Natural deduction</a></li> <li><a href="/w/index.php?title=Logical_consequence&action=edit&redlink=1" class="new" title="Logical consequence (not yet started)">Logical consequence</a></li> <li><a href="/wiki/Rule_of_inference" title="Rule of inference">Rule of inference</a></li> <li><a href="/w/index.php?title=Sequent_calculus&action=edit&redlink=1" class="new" title="Sequent calculus (not yet started)">Sequent calculus</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/w/index.php?title=Formal_system&action=edit&redlink=1" class="new" title="Formal system (not yet started)">Systems</a> <ul><li><a href="/wiki/Axiomatic_system" title="Axiomatic system">Axiomatic</a></li> <li><a href="/w/index.php?title=Deductive_system&action=edit&redlink=1" class="new" title="Deductive system (not yet started)">Deductive</a></li> <li><a href="/w/index.php?title=Hilbert_system&action=edit&redlink=1" class="new" title="Hilbert system (not yet started)">Hilbert</a> <ul><li><a href="/w/index.php?title=List_of_Hilbert_systems&action=edit&redlink=1" class="new" title="List of Hilbert systems (not yet started)">list</a></li></ul></li></ul></li> <li><a href="/w/index.php?title=Complete_theory&action=edit&redlink=1" class="new" title="Complete theory (not yet started)">Complete theory</a></li> <li><a href="/wiki/Independence_(mathematical_logic)" title="Independence (mathematical logic)">Independence</a> (<a href="/w/index.php?title=List_of_statements_independent_of_ZFC&action=edit&redlink=1" class="new" title="List of statements independent of ZFC (not yet started)">from ZFC</a>)</li> <li><a href="/w/index.php?title=Proof_of_impossibility&action=edit&redlink=1" class="new" title="Proof of impossibility (not yet started)">Proof of impossibility</a></li> <li><a href="/w/index.php?title=Ordinal_analysis&action=edit&redlink=1" class="new" title="Ordinal analysis (not yet started)">Ordinal analysis</a></li> <li><a href="/w/index.php?title=Reverse_mathematics&action=edit&redlink=1" class="new" title="Reverse mathematics (not yet started)">Reverse mathematics</a></li> <li><a href="/w/index.php?title=Self-verifying_theories&action=edit&redlink=1" class="new" title="Self-verifying theories (not yet started)">Self-verifying theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Model_theory&action=edit&redlink=1" class="new" title="Model theory (not yet started)">Model theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li> <li><a href="/w/index.php?title=Interpretation_(logic)&action=edit&redlink=1" class="new" title="Interpretation (logic) (not yet started)">Interpretation</a> <ul><li><a href="/w/index.php?title=Interpretation_function&action=edit&redlink=1" class="new" title="Interpretation function (not yet started)">Function</a></li> <li><a href="/w/index.php?title=Interpretation_(model_theory)&action=edit&redlink=1" class="new" title="Interpretation (model theory) (not yet started)">of models</a></li></ul></li> <li><a href="/w/index.php?title=Structure_(mathematical_logic)&action=edit&redlink=1" class="new" title="Structure (mathematical logic) (not yet started)">Model</a> <ul><li><a href="/w/index.php?title=Elementary_equivalence&action=edit&redlink=1" class="new" title="Elementary equivalence (not yet started)">Equivalence</a></li> <li><a href="/w/index.php?title=Finite_model_theory&action=edit&redlink=1" class="new" title="Finite model theory (not yet started)">Finite</a></li> <li><a href="/w/index.php?title=Saturated_model&action=edit&redlink=1" class="new" title="Saturated model (not yet started)">Saturated</a></li> <li><a href="/w/index.php?title=Spectrum_of_a_theory&action=edit&redlink=1" class="new" title="Spectrum of a theory (not yet started)">Spectrum</a></li> <li><a href="/w/index.php?title=Substructure_(mathematics)&action=edit&redlink=1" class="new" title="Substructure (mathematics) (not yet started)">Submodel</a></li></ul></li> <li><a href="/w/index.php?title=Non-standard_model&action=edit&redlink=1" class="new" title="Non-standard model (not yet started)">Non-standard model</a> <ul><li><a href="/w/index.php?title=Non-standard_model_of_arithmetic&action=edit&redlink=1" class="new" title="Non-standard model of arithmetic (not yet started)">of arithmetic</a></li></ul></li> <li><a href="/w/index.php?title=Diagram_(mathematical_logic)&action=edit&redlink=1" class="new" title="Diagram (mathematical logic) (not yet started)">Diagram</a> <ul><li><a href="/w/index.php?title=Elementary_diagram&action=edit&redlink=1" class="new" title="Elementary diagram (not yet started)">Elementary</a></li></ul></li> <li><a href="/w/index.php?title=Categorical_theory&action=edit&redlink=1" class="new" title="Categorical theory (not yet started)">Categorical theory</a></li> <li><a href="/w/index.php?title=Model_complete_theory&action=edit&redlink=1" class="new" title="Model complete theory (not yet started)">Model complete theory</a></li> <li><a href="/w/index.php?title=Satisfiability&action=edit&redlink=1" class="new" title="Satisfiability (not yet started)">Satisfiability</a></li> <li><a href="/w/index.php?title=Semantics_of_logic&action=edit&redlink=1" class="new" title="Semantics of logic (not yet started)">Semantics of logic</a></li> <li><a href="/w/index.php?title=Strength_(mathematical_logic)&action=edit&redlink=1" class="new" title="Strength (mathematical logic) (not yet started)">Strength</a></li> <li><a href="/w/index.php?title=Theories_of_truth&action=edit&redlink=1" class="new" title="Theories of truth (not yet started)">Theories of truth</a> <ul><li><a href="/w/index.php?title=Semantic_theory_of_truth&action=edit&redlink=1" class="new" title="Semantic theory of truth (not yet started)">Semantic</a></li> <li><a href="/w/index.php?title=Tarski%27s_theory_of_truth&action=edit&redlink=1" class="new" title="Tarski's theory of truth (not yet started)">Tarski's</a></li> <li><a href="/w/index.php?title=Kripke%27s_theory_of_truth&action=edit&redlink=1" class="new" title="Kripke's theory of truth (not yet started)">Kripke's</a></li></ul></li> <li><a href="/w/index.php?title=T-schema&action=edit&redlink=1" class="new" title="T-schema (not yet started)">T-schema</a></li> <li><a href="/w/index.php?title=Transfer_principle&action=edit&redlink=1" class="new" title="Transfer principle (not yet started)">Transfer principle</a></li> <li><a href="/w/index.php?title=Truth_predicate&action=edit&redlink=1" class="new" title="Truth predicate (not yet started)">Truth predicate</a></li> <li><a href="/w/index.php?title=Type_(model_theory)&action=edit&redlink=1" class="new" title="Type (model theory) (not yet started)">Type</a></li> <li><a href="/w/index.php?title=Ultraproduct&action=edit&redlink=1" class="new" title="Ultraproduct (not yet started)">Ultraproduct</a></li> <li><a href="/w/index.php?title=Validity_(logic)&action=edit&redlink=1" class="new" title="Validity (logic) (not yet started)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Church%E2%80%93Turing_thesis" title="Church–Turing thesis">Church–Turing thesis</a></li> <li><a href="/wiki/Computable_function" title="Computable function">Computable function</a></li> <li><a href="/wiki/Decision_problem" title="Decision problem">Decision problem</a> <ul><li><a href="/wiki/P_versus_NP_problem" title="P versus NP problem">P versus NP problem</a></li> <li><a href="/w/index.php?title=Decidability_(logic)&action=edit&redlink=1" class="new" title="Decidability (logic) (not yet started)">Decidable</a></li> <li><a href="/w/index.php?title=Undecidable_problem&action=edit&redlink=1" class="new" title="Undecidable problem (not yet started)">Undecidable</a></li> <li><a href="/w/index.php?title=P_(complexity)&action=edit&redlink=1" class="new" title="P (complexity) (not yet started)">P</a></li> <li><a href="/w/index.php?title=NP_(complexity)&action=edit&redlink=1" class="new" title="NP (complexity) (not yet started)">NP</a></li></ul></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li> <li><a href="/wiki/Recursion" title="Recursion">Recursion</a></li> <li><a href="/wiki/Turing_machine" title="Turing machine">Turing machine</a></li> <li><a href="/w/index.php?title=Church_encoding&action=edit&redlink=1" class="new" title="Church encoding (not yet started)">Church encoding</a></li> <li><a href="/w/index.php?title=Computably_enumerable_set&action=edit&redlink=1" class="new" title="Computably enumerable set (not yet started)">Computably enumerable</a></li> <li><a href="/wiki/Computable_set" class="mw-redirect" title="Computable set">Computable set</a></li> <li><a href="/w/index.php?title=Kolmogorov_complexity&action=edit&redlink=1" class="new" title="Kolmogorov complexity (not yet started)">Kolmogorov complexity</a></li> <li><a href="/w/index.php?title=Primitive_recursive_function&action=edit&redlink=1" class="new" title="Primitive recursive function (not yet started)">Primitive recursive function</a></li> <li><a href="/w/index.php?title=Recursive_set&action=edit&redlink=1" class="new" title="Recursive set (not yet started)">Recursive set</a></li> <li><a href="/w/index.php?title=Type_theory&action=edit&redlink=1" class="new" title="Type theory (not yet started)">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div 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