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</div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">类 (数学)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。30种语言可用" > <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-30" 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">30种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Classe_(matem%C3%A0tiques)" title="Classe (matemàtiques) – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Classe (matemàtiques)" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" 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/T%C5%99%C3%ADda_(matematika)" title="Třída (matematika) – 捷克语" lang="cs" hreflang="cs" data-title="Třída (matematika)" data-language-autonym="Čeština" data-language-local-name="捷克语" 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/Klasse_(matematik)" title="Klasse (matematik) – 丹麦语" lang="da" hreflang="da" data-title="Klasse (matematik)" data-language-autonym="Dansk" data-language-local-name="丹麦语" 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/Klasse_(Mengenlehre)" title="Klasse (Mengenlehre) – 德语" lang="de" hreflang="de" data-title="Klasse (Mengenlehre)" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Class_(set_theory)" title="Class (set theory) – 英语" lang="en" hreflang="en" data-title="Class (set theory)" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Clase_(teor%C3%ADa_de_conjuntos)" title="Clase (teoría de conjuntos) – 西班牙语" lang="es" hreflang="es" data-title="Clase (teoría de conjuntos)" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Klass_(matemaatika)" title="Klass (matemaatika) – 爱沙尼亚语" lang="et" hreflang="et" data-title="Klass (matemaatika)" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D9%84%D8%A7%D8%B3_(%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87%E2%80%8C%D9%87%D8%A7)" title="کلاس (نظریه مجموعه‌ها) – 波斯语" lang="fa" hreflang="fa" data-title="کلاس (نظریه مجموعه‌ها)" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Luokka_(matematiikka)" title="Luokka (matematiikka) – 芬兰语" lang="fi" hreflang="fi" data-title="Luokka (matematiikka)" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Classe_(math%C3%A9matiques)" title="Classe (mathématiques) – 法语" lang="fr" hreflang="fr" data-title="Classe (mathématiques)" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%97%D7%9C%D7%A7%D7%94_(%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%95%D7%AA)" title="מחלקה (תורת הקבוצות) – 希伯来语" lang="he" hreflang="he" data-title="מחלקה (תורת הקבוצות)" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Klasa_(matematika)" title="Klasa (matematika) – 克罗地亚语" lang="hr" hreflang="hr" data-title="Klasa (matematika)" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Oszt%C3%A1ly_(halmazelm%C3%A9let)" title="Osztály (halmazelmélet) – 匈牙利语" lang="hu" hreflang="hu" data-title="Osztály (halmazelmélet)" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%A1%D5%BD_(%D5%A2%D5%A1%D5%A6%D5%B4%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6%D5%B6%D5%A5%D6%80%D5%AB_%D5%BF%D5%A5%D5%BD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6)" title="Դաս (բազմությունների տեսություն) – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Դաս (բազմությունների տեսություն)" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kelas_(teori_himpunan)" title="Kelas (teori himpunan) – 印度尼西亚语" lang="id" hreflang="id" data-title="Kelas (teori himpunan)" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Classe_(matematica)" title="Classe (matematica) – 意大利语" lang="it" hreflang="it" data-title="Classe (matematica)" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%A9%E3%82%B9_(%E9%9B%86%E5%90%88%E8%AB%96)" title="クラス (集合論) – 日语" lang="ja" hreflang="ja" data-title="クラス (集合論)" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AA%A8%EC%9E%84_(%EC%A7%91%ED%95%A9%EB%A1%A0)" title="모임 (집합론) – 韩语" lang="ko" hreflang="ko" data-title="모임 (집합론)" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Classa_(matem%C3%A0tica)" title="Classa (matemàtica) – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Classa (matemàtica)" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Klasse_(verzamelingenleer)" title="Klasse (verzamelingenleer) – 荷兰语" lang="nl" hreflang="nl" data-title="Klasse (verzamelingenleer)" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Klasse_i_matematikk" title="Klasse i matematikk – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Klasse i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Klasa_(matematyka)" title="Klasa (matematyka) – 波兰语" lang="pl" hreflang="pl" data-title="Klasa (matematyka)" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Classe_(teoria_dos_conjuntos)" title="Classe (teoria dos conjuntos) – 葡萄牙语" lang="pt" hreflang="pt" data-title="Classe (teoria dos conjuntos)" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Clas%C4%83_(matematic%C4%83)" title="Clasă (matematică) – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Clasă (matematică)" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%81%D1%81_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Класс (математика) – 俄语" lang="ru" hreflang="ru" data-title="Класс (математика)" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Razred_(teorija_mno%C5%BEic)" title="Razred (teorija množic) – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Razred (teorija množic)" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Klass_(matematik)" title="Klass (matematik) – 瑞典语" lang="sv" hreflang="sv" data-title="Klass (matematik)" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%81%E0%AE%A4%E0%AE%BF_(%E0%AE%95%E0%AE%A3%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81)" title="தொகுதி (கணக் கோட்பாடு) – 泰米尔语" lang="ta" hreflang="ta" data-title="தொகுதி (கணக் கோட்பாடு)" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%81_(%D1%82%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD)" title="Клас (теорія множин) – 乌克兰语" lang="uk" hreflang="uk" data-title="Клас (теорія множин)" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%E1%BB%9Bp_(l%C3%BD_thuy%E1%BA%BFt_t%E1%BA%ADp_h%E1%BB%A3p)" title="Lớp (lý thuyết tập hợp) – 越南语" lang="vi" hreflang="vi" data-title="Lớp (lý thuyết tập hợp)" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q217594#sitelinks-wikipedia" title="编辑跨语言链接" 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.ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-No_footnotes plainlinks metadata ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Text_document_with_red_question_mark.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目已<a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E4%BE%86%E6%BA%90" class="mw-redirect" title="Wikipedia:列明來源">列出參考文獻</a>，但<b>因為沒有<a href="/wiki/Help:%E8%84%9A%E6%B3%A8" title="Help:脚注">文內引註</a>而使來源仍然不明</b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2022年10月9日</span>)</i></small><span class="hide-when-compact"><br /><small>请加上合适的文內引註来<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E7%B1%BB_(%E6%95%B0%E5%AD%A6)&action=edit">改善这篇条目</a>。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <div id="noteTA-8a12d924" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Math"></div></div><div class="noteTA-local"><div data-noteta-code="zh-cn:数学对象;zh-tw:數學物件;"></div></div></div> <p>在<a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a>及其<a href="/wiki/%E6%95%B8%E5%AD%B8" class="mw-redirect" title="數學">數學</a>應用中，<b>類</b>（英語：<span lang="en">class</span>）是一組<a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a>（或其他<a href="/wiki/%E6%95%B8%E5%AD%B8%E7%89%A9%E4%BB%B6" class="mw-redirect" title="數學物件">數學物件</a>）所構成的整體。有些類是集合（例如由所有<a href="/wiki/%E5%81%B6%E6%95%B0" class="mw-redirect" title="偶数">偶數</a>構成的類），但有些則不是（如所有集合所構成的類），不是集合的類被稱之為<b>真類</b>（英語：<span lang="en">proper class</span>）。有些<a href="/wiki/%E5%85%AC%E7%90%86%E5%8C%96%E9%9B%86%E5%90%88%E8%AE%BA" title="公理化集合论">公理化集合论</a>是以類為出發點來定義集合的，如<a href="/wiki/%E5%86%AF%E8%AF%BA%E4%BC%8A%E6%9B%BC-%E5%8D%9A%E5%86%85%E6%96%AF-%E5%93%A5%E5%BE%B7%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="冯诺伊曼-博内斯-哥德尔集合论">冯诺伊曼-博内斯-哥德尔集合论</a>。 </p><p>在數學裡，有許多物件對集合而言太大，而必須以類來描述，像是大的<a href="/wiki/%E7%AF%84%E7%96%87_(%E6%95%B8%E5%AD%B8)" title="範疇 (數學)">範疇</a>和<a href="/wiki/%E8%B6%85%E5%AF%A6%E6%95%B8" class="mw-redirect mw-disambig" title="超實數">超實數</a>的類體之類等。要證明一給定「事物」為一真類，一般的做法是證明此一「事物」至少有著如序數一般多的元素。有關此一證明的例子，請參見<span class="ilh-all" data-orig-title="完全自由格" data-lang-code="en" data-lang-name="英语" data-foreign-title="Free_lattice#The_complete_free_lattice"><span class="ilh-page"><a href="/w/index.php?title=%E5%AE%8C%E5%85%A8%E8%87%AA%E7%94%B1%E6%A0%BC&action=edit&redlink=1" class="new" title="完全自由格（页面不存在）">完全自由格</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Free_lattice#The_complete_free_lattice" class="extiw" title="en:Free lattice"><span lang="en" dir="auto">Free_lattice#The_complete_free_lattice</span></a></span>）</span></span>。 </p><p>真類不能是一個集合或者是一個類的元素，而且不受<a href="/wiki/%E7%AD%96%E6%A2%85%E6%B4%9B-%E5%BC%97%E5%85%B0%E5%85%8B%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="策梅洛-弗兰克尔集合论">ZF集合論</a>中的<a href="/wiki/%E5%85%AC%E7%90%86" title="公理">公理</a>所限制；因此避免掉了許多<a href="/wiki/%E6%9C%B4%E7%B4%A0%E9%9B%86%E5%90%88%E8%AE%BA" title="朴素集合论">樸素集合論</a>中的<a href="/wiki/%E6%82%96%E8%AB%96" class="mw-redirect" title="悖論">悖論</a>。反而，這些悖論成了證明某一個類是否為真類的方法之一。例如，<a href="/wiki/%E7%BE%85%E7%B4%A0%E6%82%96%E8%AB%96" class="mw-redirect" title="羅素悖論">羅素悖論</a>可以證明由所有不包含集合自身的集合所構成的類是一個真類，而<a href="/wiki/%E5%B8%83%E6%8B%89%E5%88%A9-%E7%A6%8F%E5%B0%94%E8%92%82%E6%82%96%E8%AE%BA" title="布拉利-福尔蒂悖论">布拉利-福尔蒂悖论</a>則可證明所有<a href="/wiki/%E5%BA%8F%E6%95%B8" class="mw-redirect" title="序數">序數</a>所構成的類是一個真類。 </p><p>標準的<a href="/wiki/%E7%AD%96%E6%A2%85%E7%BE%85-%E5%BC%97%E8%98%AD%E5%85%8B%E7%88%BE%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="策梅羅-弗蘭克爾集合論">ZF集合論公理</a>不會論及到類；而在<a href="/wiki/%E5%85%83%E8%AA%9E%E8%A8%80" title="元語言">元語言</a>中，類只作為<a href="/wiki/%E5%91%BD%E9%A2%98%E9%80%BB%E8%BE%91" title="命题逻辑">邏輯公式</a>的等價類而存在。<a href="/wiki/%E5%86%AF%E8%AF%BA%E4%BC%8A%E6%9B%BC-%E5%8D%9A%E5%86%85%E6%96%AF-%E5%93%A5%E5%BE%B7%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="冯诺伊曼-博内斯-哥德尔集合论">馮諾伊曼-博內斯-哥德爾集合論</a>則採取了另一種方式；類在此一理論中是基礎的物件，而集合則被定義為可以是其他某些類的元素的類。真類，則為不可以是其他任何類的元素的類。 </p><p>在其他集合論如<a href="/wiki/%E6%96%B0%E5%9F%BA%E7%A1%80%E9%9B%86%E5%90%88%E8%AE%BA" title="新基础集合论">新基础集合论</a>或<a href="/wiki/%E5%8D%8A%E9%9B%86%E5%90%88" title="半集合">半集合</a>的理論中，「真類」的概念依然是有意義的（不是任一堆事物都會是集合），但對集合特質的認定並非依據其<a href="/wiki/%E5%A4%A7%E5%B0%8F%E9%99%90%E5%88%B6%E5%85%AC%E7%90%86" title="大小限制公理">大小</a>。例如，所有包含<a href="/wiki/%E5%85%A8%E9%9B%86" title="全集">全集</a>的集合論都會有個是集合的子類的真類。 </p><p>「類」這一詞有時會和「集合」同義，最為人知的是「<a href="/wiki/%E7%AD%89%E5%83%B9%E9%A1%9E" class="mw-redirect" title="等價類">等價類</a>」這一術語。這種用法是因為從前對類和集合不如現今一樣地區別的緣故。許多19世紀之前對「類」的討論提及的實際上是集合，又或者會是個更為模糊的概念。 </p> <div class="mw-heading mw-heading2"><h2 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B1%BB_(%E6%95%B0%E5%AD%A6)&action=edit&section=1" title="编辑章节：引用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFJech2003" class="citation"><a href="/wiki/Thomas_Jech" class="mw-redirect" title="Thomas Jech">Jech, Thomas</a>, Set Theory, Springer Monographs in Mathematics third millennium, Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, 2003, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-3-540-44085-7" title="Special:网络书源/978-3-540-44085-7"><span title="国际标准书号">ISBN</span> 978-3-540-44085-7</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B1%BB+%28%E6%95%B0%E5%AD%A6%29&rft.aufirst=Thomas&rft.aulast=Jech&rft.btitle=Set+Theory&rft.date=2003&rft.edition=third+millennium&rft.genre=book&rft.isbn=978-3-540-44085-7&rft.place=Berlin%2C+New+York&rft.pub=Springer-Verlag&rft.series=Springer+Monographs+in+Mathematics&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFLevy1979" class="citation"><a href="/w/index.php?title=Azriel_Levy&action=edit&redlink=1" class="new" title="Azriel Levy（页面不存在）">Levy, A.</a>, Basic Set Theory, Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, 1979</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B1%BB+%28%E6%95%B0%E5%AD%A6%29&rft.aufirst=A.&rft.aulast=Levy&rft.btitle=Basic+Set+Theory&rft.date=1979&rft.genre=book&rft.place=Berlin%2C+New+York&rft.pub=Springer-Verlag&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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title="公理">公理</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%80%89%E6%8B%A9%E5%85%AC%E7%90%86" title="选择公理">选择</a> <ul><li><a href="/wiki/%E5%8F%AF%E6%95%B0%E9%80%89%E6%8B%A9%E5%85%AC%E7%90%86" title="可数选择公理">可数</a></li> <li><a href="/wiki/%E4%BE%9D%E8%B3%B4%E9%81%B8%E6%93%87%E5%85%AC%E7%90%86" title="依賴選擇公理">依賴</a></li></ul></li> <li><a href="/wiki/%E5%A4%96%E5%BB%B6%E5%85%AC%E7%90%86" title="外延公理">外延</a></li> <li><a href="/wiki/%E6%97%A0%E7%A9%B7%E5%85%AC%E7%90%86" title="无穷公理">无穷</a></li> <li><a href="/wiki/%E9%85%8D%E5%AF%B9%E5%85%AC%E7%90%86" title="配对公理">配对</a></li> <li><a href="/wiki/%E5%B9%82%E9%9B%86%E5%85%AC%E7%90%86" title="幂集公理">幂集</a></li> <li><a href="/wiki/%E6%AD%A3%E5%88%99%E6%80%A7%E5%85%AC%E7%90%86" title="正则性公理">正则性</a></li> <li><a href="/wiki/%E5%B9%B6%E9%9B%86%E5%85%AC%E7%90%86" title="并集公理">并集</a></li> <li><a href="/wiki/%E9%A6%AC%E4%B8%81%E5%85%AC%E7%90%86" title="馬丁公理">马丁公理</a></li></ul> <ul><li><a href="/wiki/%E5%85%AC%E7%90%86%E6%A8%A1%E5%BC%8F" title="公理模式">公理模式</a> <ul><li><a href="/wiki/%E6%9B%BF%E4%BB%A3%E5%85%AC%E7%90%86" title="替代公理">替代</a></li> <li><a href="/wiki/%E5%88%86%E7%B1%BB%E5%85%AC%E7%90%86" title="分类公理">分类</a></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/%E7%BB%B4%E6%81%A9%E5%9B%BE" title="维恩图"><img alt="Venn diagram of set intersection" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/100px-Venn_A_intersect_B.svg.png" decoding="async" width="100" height="71" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/150px-Venn_A_intersect_B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/200px-Venn_A_intersect_B.svg.png 2x" data-file-width="350" data-file-height="250" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">运算</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%AC%9B%E5%8D%A1%E5%84%BF%E7%A7%AF" title="笛卡儿积">笛卡儿积</a></li> <li><a href="/wiki/%E5%BE%B7%E6%91%A9%E6%A0%B9%E5%AE%9A%E5%BE%8B" title="德摩根定律">德摩根定律</a></li> <li><a href="/wiki/%E4%BA%A4%E9%9B%86" title="交集">交集</a></li> <li><a href="/wiki/%E5%86%AA%E9%9B%86" title="冪集">冪集</a></li> <li><a href="/wiki/%E8%A1%A5%E9%9B%86" title="补集">补集</a></li> <li><a href="/wiki/%E5%AF%B9%E7%A7%B0%E5%B7%AE" title="对称差">对称差</a></li> <li><a href="/wiki/%E5%B9%B6%E9%9B%86" title="并集">并集</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li>概念</li><li>方法</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8A%BF_(%E6%95%B0%E5%AD%A6)" title="势 (数学)">势</a></li> <li><a href="/wiki/%E5%9F%BA%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="基数 (数学)">基数</a>（<a href="/wiki/%E5%A4%A7%E5%9F%BA%E6%95%B0" title="大基数">大基数</a>）</li> <li><a class="mw-selflink selflink">类</a></li> <li><span class="ilh-all" data-orig-title="可构造全集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Constructible universe"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%AF%E6%9E%84%E9%80%A0%E5%85%A8%E9%9B%86&action=edit&redlink=1" class="new" title="可构造全集（页面不存在）">可构造全集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Constructible_universe" class="extiw" title="en:Constructible universe"><span lang="en" dir="auto">Constructible universe</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%BF%9E%E7%BB%AD%E7%BB%9F%E5%81%87%E8%AE%BE" title="连续统假设">连续统假设</a></li> <li><a href="/wiki/%E5%B0%8D%E8%A7%92%E8%AB%96%E8%AD%89%E6%B3%95" title="對角論證法">對角論證法</a></li> <li><a href="/wiki/%E5%85%83%E7%B4%A0_(%E6%95%B8%E5%AD%B8)" title="元素 (數學)">元素</a> <ul><li><a href="/wiki/%E6%9C%89%E5%BA%8F%E5%AF%B9" title="有序对">有序对</a></li> <li><a href="/wiki/%E5%85%83%E7%BB%84" title="元组">元组</a></li></ul></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E6%97%8F" title="集合族">集合族</a></li> <li><a href="/wiki/%E5%8A%9B%E8%BF%AB" title="力迫">力迫</a></li> <li><a href="/wiki/%E5%8F%8C%E5%B0%84" title="双射">一一对应</a></li> <li><a href="/wiki/%E5%BA%8F%E6%95%B0" title="序数">序数</a></li> <li><a href="/wiki/%E8%B6%85%E9%99%90%E5%BD%92%E7%BA%B3%E6%B3%95" title="超限归纳法">超限归纳法</a></li> <li><a href="/wiki/%E6%96%87%E6%B0%8F%E5%9B%BE" title="文氏图">文氏图</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a>类型</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8F%AF%E6%95%B8%E9%9B%86" title="可數集">可數集</a></li> <li><a href="/wiki/%E7%A9%BA%E9%9B%86" title="空集">空集</a></li> <li><a href="/wiki/%E6%9C%89%E9%99%90%E9%9B%86%E5%90%88" title="有限集合">有限集合</a>（<a href="/wiki/%E7%BB%A7%E6%89%BF%E6%9C%89%E9%99%90%E9%9B%86%E5%90%88" title="继承有限集合">继承有限集合</a>）</li> <li><a href="/wiki/%E6%A8%A1%E7%B3%8A%E9%9B%86" title="模糊集">模糊集</a></li> <li><a href="/wiki/%E6%97%A0%E9%99%90%E9%9B%86%E5%90%88" title="无限集合">无限集合</a></li> <li><a href="/wiki/%E9%80%92%E5%BD%92%E9%9B%86%E5%90%88" title="递归集合">递归集合</a></li> <li><a href="/wiki/%E5%AD%90%E9%9B%86" title="子集">子集</a></li> <li><a href="/wiki/%E4%BC%A0%E9%80%92%E9%9B%86%E5%90%88" title="传递集合">传递集合</a></li> <li><a href="/wiki/%E4%B8%8D%E5%8F%AF%E6%95%B8%E9%9B%86" title="不可數集">不可數集</a></li> <li><span class="ilh-all" data-orig-title="泛集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Universal set"><span class="ilh-page"><a href="/w/index.php?title=%E6%B3%9B%E9%9B%86&action=edit&redlink=1" class="new" title="泛集（页面不存在）">泛集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Universal_set" class="extiw" title="en:Universal set"><span lang="en" dir="auto">Universal set</span></a></span>）</span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">理论</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8F%AF%E6%9B%BF%E4%BB%A3%E7%9A%84%E9%9B%86%E5%90%88%E8%AE%BA" title="可替代的集合论">可替代的集合论</a></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E8%AE%BA" title="集合论">集合论</a></li> <li><a href="/wiki/%E6%9C%B4%E7%B4%A0%E9%9B%86%E5%90%88%E8%AE%BA" title="朴素集合论">朴素集合论</a></li> <li><a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94%E5%AE%9A%E7%90%86" title="康托尔定理">康托尔定理</a></li></ul> <ul><li><a href="/wiki/%E7%AD%96%E6%A2%85%E6%B4%9B%E9%9B%86%E5%90%88%E8%AE%BA" title="策梅洛集合论">策梅洛</a> <ul><li><span class="ilh-all" data-orig-title="广义集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="General set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%B9%BF%E4%B9%89%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="广义集合论（页面不存在）">广义</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/General_set_theory" class="extiw" title="en:General set theory"><span lang="en" dir="auto">General set theory</span></a></span>）</span></span></li></ul></li> <li>《<a href="/wiki/%E6%95%B0%E5%AD%A6%E5%8E%9F%E7%90%86" title="数学原理">数学原理</a>》 <ul><li><a href="/wiki/%E6%96%B0%E5%9F%BA%E7%A1%80%E9%9B%86%E5%90%88%E8%AE%BA" title="新基础集合论">新基础</a></li></ul></li> <li><a href="/wiki/%E7%AD%96%E6%A2%85%E6%B4%9B-%E5%BC%97%E5%85%B0%E5%85%8B%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="策梅洛-弗兰克尔集合论">策梅洛-弗兰克</a> <ul><li><a href="/wiki/%E5%86%AF%E8%AF%BA%E4%BC%8A%E6%9B%BC-%E5%8D%9A%E5%86%85%E6%96%AF-%E5%93%A5%E5%BE%B7%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="冯诺伊曼-博内斯-哥德尔集合论">冯诺伊曼-博内斯-哥德尔</a> <ul><li><span class="ilh-all" data-orig-title="Morse–Kelley集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Morse–Kelley set theory"><span class="ilh-page"><a href="/w/index.php?title=Morse%E2%80%93Kelley%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="Morse–Kelley集合论（页面不存在）">Morse–Kelley</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Morse%E2%80%93Kelley_set_theory" class="extiw" title="en:Morse–Kelley set theory"><span lang="en" dir="auto">Morse–Kelley set theory</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="克里普克–普拉特克集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kripke–Platek set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%8B%E9%87%8C%E6%99%AE%E5%85%8B%E2%80%93%E6%99%AE%E6%8B%89%E7%89%B9%E5%85%8B%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="克里普克–普拉特克集合论（页面不存在）">克里普克–普拉特克</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kripke%E2%80%93Platek_set_theory" class="extiw" title="en:Kripke–Platek set theory"><span lang="en" dir="auto">Kripke–Platek set theory</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="塔斯基–格罗滕迪克集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tarski–Grothendieck set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%A1%94%E6%96%AF%E5%9F%BA%E2%80%93%E6%A0%BC%E7%BD%97%E6%BB%95%E8%BF%AA%E5%85%8B%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="塔斯基–格罗滕迪克集合论（页面不存在）">塔斯基–格罗滕迪克</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tarski%E2%80%93Grothendieck_set_theory" class="extiw" title="en:Tarski–Grothendieck set theory"><span lang="en" dir="auto">Tarski–Grothendieck set theory</span></a></span>）</span></span></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li><span class="ilh-all" data-orig-title="集合论悖论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Paradoxes of set theory"><span class="ilh-page"><a href="/w/index.php?title=%E9%9B%86%E5%90%88%E8%AE%BA%E6%82%96%E8%AE%BA&action=edit&redlink=1" class="new" title="集合论悖论（页面不存在）">悖论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Paradoxes_of_set_theory" class="extiw" title="en:Paradoxes of set theory"><span lang="en" dir="auto">Paradoxes of set theory</span></a></span>）</span></span></li><li>问题</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%BD%97%E7%B4%A0%E6%82%96%E8%AE%BA" title="罗素悖论">罗素悖论</a></li> <li><a href="/wiki/%E8%98%87%E6%96%AF%E6%9E%97%E5%95%8F%E9%A1%8C" title="蘇斯林問題">蘇斯林問題</a></li> <li><a href="/wiki/ZFC%E7%B3%BB%E7%B5%B1%E7%84%A1%E6%B3%95%E7%A2%BA%E5%AE%9A%E7%9A%84%E5%91%BD%E9%A1%8C%E5%88%97%E8%A1%A8" title="ZFC系統無法確定的命題列表">ZFC系統無法確定的命題列表</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:%E9%9B%86%E5%90%88%E8%AB%96%E8%80%85" title="Category:集合論者">集合論者</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BA%9A%E4%BC%AF%E6%8B%89%E7%BD%95%C2%B7%E5%BC%97%E5%85%B0%E5%85%8B%E5%B0%94" title="亚伯拉罕·弗兰克尔">亚伯拉罕·弗兰克尔</a></li> <li><a href="/wiki/%E4%BC%AF%E7%89%B9%E5%85%B0%C2%B7%E7%BD%97%E7%B4%A0" title="伯特兰·罗素">伯特兰·罗素</a></li> <li><a href="/wiki/%E6%81%A9%E6%96%AF%E7%89%B9%C2%B7%E7%AD%96%E6%A2%85%E6%B4%9B" title="恩斯特·策梅洛">恩斯特·策梅洛</a></li> <li><a href="/wiki/%E6%A0%BC%E5%A5%A5%E5%B0%94%E6%A0%BC%C2%B7%E5%BA%B7%E6%89%98%E5%B0%94" title="格奥尔格·康托尔">格奥尔格·康托尔</a></li> <li><a href="/wiki/%E7%BA%A6%E7%BF%B0%C2%B7%E5%86%AF%C2%B7%E8%AF%BA%E4%BC%8A%E6%9B%BC" class="mw-redirect" title="约翰·冯·诺伊曼">约翰·冯·诺伊曼</a></li> <li><a href="/wiki/%E5%BA%93%E5%B0%94%E7%89%B9%C2%B7%E5%93%A5%E5%BE%B7%E5%B0%94" title="库尔特·哥德尔">库尔特·哥德尔</a></li> <li><a href="/wiki/%E7%9B%A7%E8%8F%B2%E7%89%B9%C2%B7%E6%BE%A4%E5%BE%B7" class="mw-redirect" title="盧菲特·澤德">盧菲特·澤德</a></li> <li><span class="ilh-all" data-orig-title="保罗·贝尔奈斯" data-lang-code="en" data-lang-name="英语" data-foreign-title="Paul Bernays"><span class="ilh-page"><a href="/w/index.php?title=%E4%BF%9D%E7%BD%97%C2%B7%E8%B4%9D%E5%B0%94%E5%A5%88%E6%96%AF&action=edit&redlink=1" class="new" title="保罗·贝尔奈斯（页面不存在）">保罗·贝尔奈斯</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Paul_Bernays" class="extiw" title="en:Paul Bernays"><span lang="en" dir="auto">Paul Bernays</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E5%AF%87%E6%81%A9" title="保罗·寇恩">保罗·寇恩</a></li> <li><a href="/wiki/%E7%90%86%E6%9F%A5%E5%BE%B7%C2%B7%E6%88%B4%E5%BE%B7%E9%87%91" title="理查德·戴德金">理查德·戴德金</a></li> <li><a href="/wiki/%E6%89%98%E9%A9%AC%E4%BB%80%C2%B7%E8%80%B6%E8%B5%AB" 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