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class="vector-toc-link" href="#Large_cardinals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Large cardinals</span> </div> </a> <ul id="toc-Large_cardinals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Recursion_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Recursion_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Recursion theory</span> </div> </a> <ul id="toc-Recursion_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proof_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Proof_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Proof theory</span> </div> </a> <ul id="toc-Proof_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematical_constructivism" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematical_constructivism"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Mathematical constructivism</span> </div> </a> <ul id="toc-Mathematical_constructivism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modal_logic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modal_logic"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Modal logic</span> </div> </a> <ul id="toc-Modal_logic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theorem_provers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theorem_provers"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Theorem provers</span> </div> </a> <ul id="toc-Theorem_provers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discovery_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Discovery_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Discovery systems</span> </div> </a> <ul id="toc-Discovery_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historical" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historical"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Historical</span> </div> </a> <ul id="toc-Historical-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> </ul> 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable plainlinks selfreference noprint">Clicking on <i><b>related changes</b></i> shows a list of most-recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in <i>related changes</i>.</div> <p>This is a <b>list of <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a> topics</b>. </p><p>For traditional syllogistic logic, see the <a href="/wiki/List_of_topics_in_logic" class="mw-redirect" title="List of topics in logic">list of topics in logic</a>. See also the <a href="/wiki/List_of_computability_and_complexity_topics" title="List of computability and complexity topics">list of computability and complexity topics</a> for more theory of <a href="/wiki/Algorithm" title="Algorithm">algorithms</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Working_foundations">Working foundations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=1" title="Edit section: Working foundations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Peano_axioms" title="Peano axioms">Peano axioms</a> <ul><li><a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a></li></ul></li> <li><a href="/wiki/Mathematical_induction" title="Mathematical induction">Mathematical induction</a> <ul><li><a href="/wiki/Structural_induction" title="Structural induction">Structural induction</a></li> <li><a href="/wiki/Recursive_definition" title="Recursive definition">Recursive definition</a></li></ul></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive set theory</a> <ul><li><a href="/wiki/Element_(mathematics)" title="Element (mathematics)">Element (mathematics)</a> <ul><li><a href="/wiki/Ur-element" class="mw-redirect" title="Ur-element">Ur-element</a></li></ul></li> <li><a href="/wiki/Singleton_(mathematics)" title="Singleton (mathematics)">Singleton (mathematics)</a></li> <li><a href="/wiki/Simple_theorems_in_the_algebra_of_sets" title="Simple theorems in the algebra of sets">Simple theorems in the algebra of sets</a></li> <li><a href="/wiki/Algebra_of_sets" title="Algebra of sets">Algebra of sets</a></li> <li><a href="/wiki/Power_set" title="Power set">Power set</a></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty set</a></li> <li><a href="/wiki/Non-empty_set" class="mw-redirect" title="Non-empty set">Non-empty set</a></li> <li><a href="/wiki/Empty_function" class="mw-redirect" title="Empty function">Empty function</a></li></ul></li> <li><a href="/wiki/Universe_(mathematics)" title="Universe (mathematics)">Universe (mathematics)</a></li> <li><a href="/wiki/Axiomatization" class="mw-redirect" title="Axiomatization">Axiomatization</a></li> <li><a href="/wiki/Axiomatic_system" title="Axiomatic system">Axiomatic system</a> <ul><li><a href="/wiki/Axiom_schema" title="Axiom schema">Axiom schema</a></li></ul></li> <li><a href="/wiki/Axiomatic_method" class="mw-redirect" title="Axiomatic method">Axiomatic method</a></li> <li><a href="/wiki/Formal_system" title="Formal system">Formal system</a></li> <li><a href="/wiki/Mathematical_proof" title="Mathematical proof">Mathematical proof</a> <ul><li><a href="/wiki/Direct_proof" title="Direct proof">Direct proof</a></li> <li><a href="/wiki/Reductio_ad_absurdum" title="Reductio ad absurdum">Reductio ad absurdum</a></li> <li><a href="/wiki/Proof_by_exhaustion" title="Proof by exhaustion">Proof by exhaustion</a></li> <li><a href="/wiki/Constructive_proof" title="Constructive proof">Constructive proof</a></li> <li><a href="/wiki/Nonconstructive_proof" class="mw-redirect" title="Nonconstructive proof">Nonconstructive proof</a></li></ul></li> <li><a href="/wiki/Tautology_(logic)" title="Tautology (logic)">Tautology</a></li> <li><a href="/wiki/Consistency_proof" class="mw-redirect" title="Consistency proof">Consistency proof</a></li> <li><a href="/wiki/Arithmetization_of_analysis" title="Arithmetization of analysis">Arithmetization of analysis</a></li> <li><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations of mathematics</a></li> <li><a href="/wiki/Formal_language" title="Formal language">Formal language</a></li> <li><i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i></li> <li><a href="/wiki/Hilbert%27s_program" title="Hilbert's program">Hilbert's program</a></li> <li><a href="/wiki/Impredicative" class="mw-redirect" title="Impredicative">Impredicative</a></li> <li><a href="/wiki/Definable_real_number" title="Definable real number">Definable real number</a></li> <li><a href="/wiki/Algebraic_logic" title="Algebraic logic">Algebraic logic</a> <ul><li><a href="/wiki/Boolean_algebra_(logic)" class="mw-redirect" title="Boolean algebra (logic)">Boolean algebra (logic)</a></li></ul></li> <li><a href="/wiki/Dialectica_space" title="Dialectica space">Dialectica space</a></li> <li><a href="/wiki/Categorical_logic" title="Categorical logic">categorical logic</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Model_theory">Model theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=2" title="Edit section: Model theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Finite_model_theory" title="Finite model theory">Finite model theory</a> <ul><li><a href="/wiki/Descriptive_complexity_theory" title="Descriptive complexity theory">Descriptive complexity theory</a></li> <li><a href="/wiki/Model_checking" title="Model checking">Model checking</a></li> <li><a href="/wiki/Trakhtenbrot%27s_theorem" title="Trakhtenbrot's theorem">Trakhtenbrot's theorem</a></li></ul></li> <li><a href="/wiki/Computable_model_theory" title="Computable model theory">Computable model theory</a> <ul><li><a href="/wiki/Tarski%27s_exponential_function_problem" title="Tarski's exponential function problem">Tarski's exponential function problem</a></li> <li><a href="/wiki/Undecidable_problem" title="Undecidable problem">Undecidable problem</a></li></ul></li> <li><a href="/wiki/Institutional_model_theory" title="Institutional model theory">Institutional model theory</a> <ul><li><a href="/wiki/Institution_(computer_science)" title="Institution (computer science)">Institution (computer science)</a></li></ul></li> <li><a href="/wiki/Non-standard_analysis" class="mw-redirect" title="Non-standard analysis">Non-standard analysis</a> <ul><li><a href="/wiki/Non-standard_calculus" class="mw-redirect" title="Non-standard calculus">Non-standard calculus</a></li> <li><a href="/wiki/Hyperinteger" title="Hyperinteger">Hyperinteger</a></li> <li><a href="/wiki/Hyperreal_number" title="Hyperreal number">Hyperreal number</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Overspill" title="Overspill">Overspill</a></li> <li><a href="/wiki/Elementary_Calculus:_An_Infinitesimal_Approach" title="Elementary Calculus: An Infinitesimal Approach">Elementary Calculus: An Infinitesimal Approach</a></li> <li><a href="/wiki/Criticism_of_non-standard_analysis" class="mw-redirect" title="Criticism of non-standard analysis">Criticism of non-standard analysis</a></li> <li><a href="/wiki/Standard_part_function" title="Standard part function">Standard part function</a></li></ul></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a> <ul><li><a href="/wiki/Forcing_(mathematics)" title="Forcing (mathematics)">Forcing (mathematics)</a> <ul><li><a href="/wiki/Boolean-valued_model" title="Boolean-valued model">Boolean-valued model</a></li></ul></li></ul></li> <li><a href="/wiki/Kripke_semantics" title="Kripke semantics">Kripke semantics</a> <ul><li><a href="/wiki/General_frame" title="General frame">General frame</a></li></ul></li> <li><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate logic</a> <ul><li><a href="/wiki/First-order_logic" title="First-order logic">First-order logic</a> <ul><li><a href="/wiki/Infinitary_logic" title="Infinitary logic">Infinitary logic</a></li> <li><a href="/wiki/Many-sorted_logic" title="Many-sorted logic">Many-sorted logic</a></li></ul></li> <li><a href="/wiki/Higher-order_logic" title="Higher-order logic">Higher-order logic</a> <ul><li><a href="/wiki/Lindstr%C3%B6m_quantifier" title="Lindström quantifier">Lindström quantifier</a></li> <li><a href="/wiki/Second-order_logic" title="Second-order logic">Second-order logic</a></li></ul></li></ul></li> <li><a href="/wiki/Soundness_theorem" class="mw-redirect" title="Soundness theorem">Soundness theorem</a></li> <li><a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">Gödel's completeness theorem</a> <ul><li><a href="/wiki/Original_proof_of_G%C3%B6del%27s_completeness_theorem" title="Original proof of Gödel's completeness theorem">Original proof of Gödel's completeness theorem</a></li></ul></li> <li><a href="/wiki/Compactness_theorem" title="Compactness theorem">Compactness theorem</a></li> <li><a href="/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem" title="Löwenheim–Skolem theorem">Löwenheim–Skolem theorem</a> <ul><li><a href="/wiki/Skolem%27s_paradox" title="Skolem's paradox">Skolem's paradox</a></li></ul></li> <li><a href="/wiki/G%C3%B6del%27s_incompleteness_theorems" title="Gödel's incompleteness theorems">Gödel's incompleteness theorems</a></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Structure (mathematical logic)</a></li> <li><a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">Interpretation (logic)</a></li> <li><a href="/wiki/Substructure_(mathematics)" title="Substructure (mathematics)">Substructure (mathematics)</a></li> <li><a href="/wiki/Elementary_substructure" class="mw-redirect" title="Elementary substructure">Elementary substructure</a> <ul><li><a href="/wiki/Skolem_hull" class="mw-redirect" title="Skolem hull">Skolem hull</a></li></ul></li> <li><a href="/wiki/Non-standard_model" title="Non-standard model">Non-standard model</a></li> <li><a href="/wiki/Atomic_model_(mathematical_logic)" title="Atomic model (mathematical logic)">Atomic model (mathematical logic)</a></li> <li><a href="/wiki/Prime_model" title="Prime model">Prime model</a></li> <li><a href="/wiki/Saturated_model" title="Saturated model">Saturated model</a></li> <li><a href="/wiki/Existentially_closed_model" title="Existentially closed model">Existentially closed model</a></li> <li><a href="/wiki/Ultraproduct" title="Ultraproduct">Ultraproduct</a></li> <li><a href="/wiki/Age_(model_theory)" class="mw-redirect" title="Age (model theory)">Age (model theory)</a> <ul><li><a href="/wiki/Amalgamation_property" title="Amalgamation property">Amalgamation property</a></li> <li><a href="/wiki/Hrushovski_construction" title="Hrushovski construction">Hrushovski construction</a></li></ul></li> <li><a href="/wiki/Potential_isomorphism" title="Potential isomorphism">Potential isomorphism</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory (mathematical logic)</a> <ul><li><a href="/wiki/Complete_theory" title="Complete theory">Complete theory</a> <ul><li><a href="/wiki/Vaught%27s_test" class="mw-redirect" title="Vaught's test">Vaught's test</a></li></ul></li> <li><a href="/wiki/Morley%27s_categoricity_theorem" class="mw-redirect" title="Morley's categoricity theorem">Morley's categoricity theorem</a> <ul><li><a href="/wiki/Stability_spectrum" title="Stability spectrum">Stability spectrum</a> <ul><li><a href="/wiki/Morley_rank" title="Morley rank">Morley rank</a></li> <li><a href="/wiki/Stable_theory" title="Stable theory">Stable theory</a> <ul><li><a href="/wiki/Forking_extension" title="Forking extension">Forking extension</a></li> <li><a href="/wiki/Strongly_minimal_theory" title="Strongly minimal theory">Strongly minimal theory</a></li> <li><a href="/wiki/Stable_group" title="Stable group">Stable group</a> <ul><li><a href="/wiki/Tame_group" title="Tame group">Tame group</a></li></ul></li></ul></li></ul></li> <li><a href="/wiki/O-minimal_theory" title="O-minimal theory">o-minimal theory</a></li> <li><a href="/wiki/Weakly_o-minimal_structure" title="Weakly o-minimal structure">Weakly o-minimal structure</a></li> <li><a href="/wiki/C-minimal_theory" title="C-minimal theory">C-minimal theory</a></li> <li><a href="/wiki/Spectrum_of_a_theory" title="Spectrum of a theory">Spectrum of a theory</a> <ul><li><a href="/wiki/Vaught_conjecture" title="Vaught conjecture">Vaught conjecture</a></li></ul></li></ul></li> <li><a href="/wiki/Model_complete_theory" title="Model complete theory">Model complete theory</a></li> <li><a href="/wiki/List_of_first-order_theories" title="List of first-order theories">List of first-order theories</a></li> <li><a href="/wiki/Conservative_extension" title="Conservative extension">Conservative extension</a></li> <li><a href="/wiki/Elementary_class" title="Elementary class">Elementary class</a> <ul><li><a href="/wiki/Pseudoelementary_class" title="Pseudoelementary class">Pseudoelementary class</a></li> <li><a href="/wiki/Strength_(mathematical_logic)" title="Strength (mathematical logic)">Strength (mathematical logic)</a></li></ul></li></ul></li> <li><a href="/wiki/Differentially_closed_field" title="Differentially closed field">Differentially closed field</a></li> <li><a href="/wiki/Exponential_field" title="Exponential field">Exponential field</a></li> <li><a href="/wiki/Ax%E2%80%93Grothendieck_theorem" title="Ax–Grothendieck theorem">Ax–Grothendieck theorem</a></li> <li><a href="/wiki/Ax%E2%80%93Kochen_theorem" title="Ax–Kochen theorem">Ax–Kochen theorem</a></li> <li><a href="/wiki/Peano_axioms" title="Peano axioms">Peano axioms</a></li> <li><a href="/wiki/Non-standard_model_of_arithmetic" title="Non-standard model of arithmetic">Non-standard model of arithmetic</a></li> <li><a href="/wiki/First-order_arithmetic" class="mw-redirect" title="First-order arithmetic">First-order arithmetic</a></li> <li><a href="/wiki/Second-order_arithmetic" title="Second-order arithmetic">Second-order arithmetic</a></li> <li><a href="/wiki/Presburger_arithmetic" title="Presburger arithmetic">Presburger arithmetic</a></li> <li><a href="/wiki/Wilkie%27s_theorem" title="Wilkie's theorem">Wilkie's theorem</a></li> <li><a href="/wiki/Functional_predicate" title="Functional predicate">Functional predicate</a></li> <li><a href="/wiki/T-schema" title="T-schema">T-schema</a></li> <li><a href="/wiki/Back-and-forth_method" title="Back-and-forth method">Back-and-forth method</a></li> <li><a href="/wiki/Barwise_compactness_theorem" title="Barwise compactness theorem">Barwise compactness theorem</a></li> <li><a href="/wiki/Skolem_normal_form" title="Skolem normal form">Skolemization</a></li> <li><a href="/wiki/Lindenbaum%E2%80%93Tarski_algebra" title="Lindenbaum–Tarski algebra">Lindenbaum–Tarski algebra</a></li> <li><a href="/wiki/L%C3%B6b%27s_theorem" title="Löb's theorem">Löb's theorem</a></li> <li><a href="/wiki/Arithmetical_set" title="Arithmetical set">Arithmetical set</a></li> <li><a href="/wiki/Definable_set" title="Definable set">Definable set</a></li> <li><a href="/wiki/Ehrenfeucht%E2%80%93Fra%C3%AFss%C3%A9_game" title="Ehrenfeucht–Fraïssé game">Ehrenfeucht–Fraïssé game</a></li> <li><a href="/wiki/Herbrand_interpretation" title="Herbrand interpretation">Herbrand interpretation</a> / <a href="/wiki/Herbrand_structure" title="Herbrand structure">Herbrand structure</a></li> <li><a href="/wiki/Imaginary_element" title="Imaginary element">Imaginary element</a></li> <li><a href="/wiki/Indiscernibles" title="Indiscernibles">Indiscernibles</a></li> <li><a href="/wiki/Interpretation_(model_theory)" title="Interpretation (model theory)">Interpretation (model theory)</a> / <a href="/wiki/Interpretable_structure" class="mw-redirect" title="Interpretable structure">Interpretable structure</a></li> <li><a href="/wiki/Pregeometry_(model_theory)" title="Pregeometry (model theory)">Pregeometry (model theory)</a></li> <li><a href="/wiki/Quantifier_elimination" title="Quantifier elimination">Quantifier elimination</a></li> <li><a href="/wiki/Reduct" title="Reduct">Reduct</a></li> <li><a href="/wiki/Signature_(logic)" title="Signature (logic)">Signature (logic)</a></li> <li><a href="/wiki/Skolem_normal_form" title="Skolem normal form">Skolem normal form</a></li> <li><a href="/wiki/Type_(model_theory)" title="Type (model theory)">Type (model theory)</a></li> <li><a href="/wiki/Zariski_geometry" title="Zariski geometry">Zariski geometry</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Set_theory">Set theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=3" title="Edit section: Set theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Algebra_of_sets" title="Algebra of sets">Algebra of sets</a> <a href="/wiki/Talk:Algebra_of_sets" title="Talk:Algebra of sets"> </a></li> <li><a href="/wiki/Axiom_of_choice" title="Axiom of choice">Axiom of choice</a> <a href="/wiki/Talk:Axiom_of_choice" title="Talk:Axiom of choice"> </a> <ul><li><a href="/wiki/Axiom_of_countable_choice" title="Axiom of countable choice">Axiom of countable choice</a> <a href="/wiki/Talk:Axiom_of_countable_choice" title="Talk:Axiom of countable choice"> </a></li> <li><a href="/wiki/Axiom_of_dependent_choice" title="Axiom of dependent choice">Axiom of dependent choice</a> <a href="/wiki/Talk:Axiom_of_dependent_choice" title="Talk:Axiom of dependent choice"> </a></li> <li><a href="/wiki/Zorn%27s_lemma" title="Zorn's lemma">Zorn's lemma</a> <a href="/wiki/Talk:Zorn%27s_lemma" title="Talk:Zorn's lemma"> </a></li></ul></li> <li><a href="/wiki/Boolean_algebra_(structure)" title="Boolean algebra (structure)">Boolean algebra (structure)</a></li> <li><a href="/wiki/Boolean-valued_model" title="Boolean-valued model">Boolean-valued model</a> <a href="/wiki/Talk:Boolean-valued_model" title="Talk:Boolean-valued model"> </a></li> <li><a href="/wiki/Burali-Forti_paradox" title="Burali-Forti paradox">Burali-Forti paradox</a> <a href="/wiki/Talk:Burali-Forti_paradox" title="Talk:Burali-Forti paradox"> </a></li> <li><a href="/wiki/Cantor%27s_back-and-forth_method" class="mw-redirect" title="Cantor's back-and-forth method">Cantor's back-and-forth method</a> <a href="/w/index.php?title=Talk:Cantor%27s_back-and-forth_method&action=edit&redlink=1" class="new" title="Talk:Cantor's back-and-forth method (page does not exist)"> </a></li> <li><a href="/wiki/Cantor%27s_diagonal_argument" title="Cantor's diagonal argument">Cantor's diagonal argument</a> <a href="/wiki/Talk:Cantor%27s_diagonal_argument" title="Talk:Cantor's diagonal argument"> </a></li> <li><a href="/wiki/Cantor%27s_first_uncountability_proof" class="mw-redirect" title="Cantor's first uncountability proof">Cantor's first uncountability proof</a> <a href="/wiki/Talk:Cantor%27s_first_uncountability_proof" class="mw-redirect" title="Talk:Cantor's first uncountability proof"> </a></li> <li><a href="/wiki/Cantor%27s_theorem" title="Cantor's theorem">Cantor's theorem</a> <a href="/wiki/Talk:Cantor%27s_theorem" title="Talk:Cantor's theorem"> </a></li> <li><a href="/wiki/Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem" class="mw-redirect" title="Cantor–Bernstein–Schroeder theorem">Cantor–Bernstein–Schroeder theorem</a> <a href="/wiki/Talk:Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem" class="mw-redirect" title="Talk:Cantor–Bernstein–Schroeder theorem"> </a></li> <li><a href="/wiki/Cardinality" title="Cardinality">Cardinality</a> <a href="/wiki/Talk:Cardinality" title="Talk:Cardinality"> </a> <ul><li><a href="/wiki/Aleph_number" title="Aleph number">Aleph number</a> <a href="/wiki/Talk:Aleph_number" title="Talk:Aleph number"> </a> <ul><li><a href="/wiki/Aleph-null" class="mw-redirect" title="Aleph-null">Aleph-null</a> <a href="/w/index.php?title=Talk:Aleph-null&action=edit&redlink=1" class="new" title="Talk:Aleph-null (page does not exist)"> </a></li> <li><a href="/wiki/Aleph-one" class="mw-redirect" title="Aleph-one">Aleph-one</a> <a href="/wiki/Talk:Aleph-one" title="Talk:Aleph-one"> </a></li></ul></li> <li><a href="/wiki/Beth_number" title="Beth number">Beth number</a> <a href="/wiki/Talk:Beth_number" title="Talk:Beth number"> </a></li> <li><a href="/wiki/Cardinal_number" title="Cardinal number">Cardinal number</a> <a href="/wiki/Talk:Cardinal_number" title="Talk:Cardinal number"> </a></li> <li><a href="/wiki/Hartogs_number" title="Hartogs number">Hartogs number</a> <a href="/wiki/Talk:Hartogs_number" title="Talk:Hartogs number"> </a></li></ul></li> <li><a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a> <a href="/wiki/Talk:Cartesian_product" title="Talk:Cartesian product"> </a></li> <li><a href="/wiki/Class_(set_theory)" title="Class (set theory)">Class (set theory)</a> <a href="/wiki/Talk:Class_(set_theory)" title="Talk:Class (set theory)"> </a></li> <li><a href="/wiki/Complement_(set_theory)" title="Complement (set theory)">Complement (set theory)</a> <a href="/wiki/Talk:Complement_(set_theory)" title="Talk:Complement (set theory)"> </a></li> <li><a href="/wiki/Complete_Boolean_algebra" title="Complete Boolean algebra">Complete Boolean algebra</a> <a href="/wiki/Talk:Complete_Boolean_algebra" title="Talk:Complete Boolean algebra"> </a></li> <li><a href="/wiki/Continuum_(set_theory)" title="Continuum (set theory)">Continuum (set theory)</a> <a href="/wiki/Talk:Continuum_(set_theory)" title="Talk:Continuum (set theory)"> </a> <ul><li><a href="/wiki/Suslin%27s_problem" title="Suslin's problem">Suslin's problem</a> <a href="/wiki/Talk:Suslin%27s_problem" title="Talk:Suslin's problem"> </a></li></ul></li> <li><a href="/wiki/Continuum_hypothesis" title="Continuum hypothesis">Continuum hypothesis</a> <a href="/wiki/Talk:Continuum_hypothesis" title="Talk:Continuum hypothesis"> </a></li> <li><a href="/wiki/Countable_set" title="Countable set">Countable set</a> <a href="/wiki/Talk:Countable_set" title="Talk:Countable set"> </a></li> <li><a href="/wiki/Descriptive_set_theory" title="Descriptive set theory">Descriptive set theory</a> <a href="/wiki/Talk:Descriptive_set_theory" title="Talk:Descriptive set theory"> </a> <ul><li><a href="/wiki/Analytic_set" title="Analytic set">Analytic set</a> <a href="/wiki/Talk:Analytic_set" title="Talk:Analytic set"> </a></li> <li><a href="/wiki/Analytical_hierarchy" title="Analytical hierarchy">Analytical hierarchy</a> <a href="/wiki/Talk:Analytical_hierarchy" title="Talk:Analytical hierarchy"> </a></li> <li><a href="/wiki/Borel_equivalence_relation" title="Borel equivalence relation">Borel equivalence relation</a> <a href="/wiki/Talk:Borel_equivalence_relation" title="Talk:Borel equivalence relation"> </a></li> <li><a href="/wiki/Infinity-Borel_set" title="Infinity-Borel set">Infinity-Borel set</a> <a href="/wiki/Talk:Infinity-Borel_set" title="Talk:Infinity-Borel set"> </a></li> <li><a href="/wiki/Lightface_analytic_game" title="Lightface analytic game">Lightface analytic game</a> <a href="/wiki/Talk:Lightface_analytic_game" title="Talk:Lightface analytic game"> </a></li> <li><a href="/wiki/Perfect_set_property" title="Perfect set property">Perfect set property</a> <a href="/wiki/Talk:Perfect_set_property" title="Talk:Perfect set property"> </a></li> <li><a href="/wiki/Polish_space" title="Polish space">Polish space</a> <a href="/wiki/Talk:Polish_space" title="Talk:Polish space"> </a></li> <li><a href="/wiki/Prewellordering" title="Prewellordering">Prewellordering</a> <a href="/wiki/Talk:Prewellordering" title="Talk:Prewellordering"> </a></li> <li><a href="/wiki/Projective_set" class="mw-redirect" title="Projective set">Projective set</a> <a href="/wiki/Talk:Projective_set" class="mw-redirect" title="Talk:Projective set"> </a></li> <li><a href="/wiki/Property_of_Baire" title="Property of Baire">Property of Baire</a> <a href="/wiki/Talk:Property_of_Baire" title="Talk:Property of Baire"> </a></li> <li><a href="/wiki/Uniformization_(set_theory)" title="Uniformization (set theory)">Uniformization (set theory)</a> <a href="/wiki/Talk:Uniformization_(set_theory)" title="Talk:Uniformization (set theory)"> </a></li> <li><a href="/wiki/Universally_measurable_set" title="Universally measurable set">Universally measurable set</a> <a href="/wiki/Talk:Universally_measurable_set" title="Talk:Universally measurable set"> </a></li></ul></li> <li><a href="/wiki/Determinacy" title="Determinacy">Determinacy</a> <a href="/wiki/Talk:Determinacy" title="Talk:Determinacy"> </a> <ul><li><a href="/wiki/AD%2B" title="AD+">AD+</a> <a href="/w/index.php?title=Talk:AD_plus&action=edit&redlink=1" class="new" title="Talk:AD plus (page does not exist)"> </a></li> <li><a href="/wiki/Axiom_of_determinacy" title="Axiom of determinacy">Axiom of determinacy</a> <a href="/wiki/Talk:Axiom_of_determinacy" title="Talk:Axiom of determinacy"> </a></li> <li><a href="/wiki/Axiom_of_projective_determinacy" title="Axiom of projective determinacy">Axiom of projective determinacy</a> <a href="/wiki/Talk:Axiom_of_projective_determinacy" title="Talk:Axiom of projective determinacy"> </a></li> <li><a href="/wiki/Axiom_of_real_determinacy" title="Axiom of real determinacy">Axiom of real determinacy</a> <a href="/wiki/Talk:Axiom_of_real_determinacy" title="Talk:Axiom of real determinacy"> </a></li></ul></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty set</a> <a href="/wiki/Talk:Empty_set" title="Talk:Empty set"> </a></li> <li><a href="/wiki/Forcing_(mathematics)" title="Forcing (mathematics)">Forcing (mathematics)</a> <a href="/wiki/Talk:Forcing_(mathematics)" title="Talk:Forcing (mathematics)"> </a></li> <li><a href="/wiki/Fuzzy_set" title="Fuzzy set">Fuzzy set</a> <a href="/wiki/Talk:Fuzzy_set" title="Talk:Fuzzy set"> </a></li> <li><a href="/wiki/Internal_set_theory" title="Internal set theory">Internal set theory</a> <a href="/wiki/Talk:Internal_set_theory" title="Talk:Internal set theory"> </a></li> <li><a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">Intersection (set theory)</a> <a href="/wiki/Talk:Intersection_(set_theory)" title="Talk:Intersection (set theory)"> </a></li> <li><a href="/wiki/Constructible_universe" title="Constructible universe">L</a> <a href="/wiki/Talk:Constructible_universe" title="Talk:Constructible universe"> </a></li> <li><a href="/wiki/L(R)" title="L(R)">L(R)</a> <a href="/wiki/Talk:L(R)" title="Talk:L(R)"> </a></li> <li><a href="/wiki/Large_cardinal_property" class="mw-redirect" title="Large cardinal property">Large cardinal property</a> <a href="/wiki/Talk:Large_cardinal_property" class="mw-redirect" title="Talk:Large cardinal property"> </a></li> <li><a href="/wiki/Set_theory_(music)" title="Set theory (music)">Musical set theory</a> <a href="/wiki/Talk:Set_theory_(music)" title="Talk:Set theory (music)"> </a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a> <a href="/wiki/Talk:Ordinal_number" title="Talk:Ordinal number"> </a> <ul><li><a href="/wiki/Infinite_descending_chain" class="mw-redirect" title="Infinite descending chain">Infinite descending chain</a> <a href="/wiki/Talk:Infinite_descending_chain" title="Talk:Infinite descending chain"> </a></li> <li><a href="/wiki/Limit_ordinal" title="Limit ordinal">Limit ordinal</a> <a href="/wiki/Talk:Limit_ordinal" title="Talk:Limit ordinal"> </a></li> <li><a href="/wiki/Successor_ordinal" title="Successor ordinal">Successor ordinal</a> <a href="/wiki/Talk:Successor_ordinal" title="Talk:Successor ordinal"> </a></li> <li><a href="/wiki/Transfinite_induction" title="Transfinite induction">Transfinite induction</a> <a href="/wiki/Talk:Transfinite_induction" title="Talk:Transfinite induction"> </a> <ul><li><a href="/wiki/%E2%88%88-induction" class="mw-redirect" title="∈-induction">∈-induction</a> <a href="/w/index.php?title=Talk:%E2%88%88-induction&action=edit&redlink=1" class="new" title="Talk:∈-induction (page does not exist)"> </a></li></ul></li> <li><a href="/wiki/Well-founded_set" class="mw-redirect" title="Well-founded set">Well-founded set</a> <a href="/w/index.php?title=Talk:Well-founded_set&action=edit&redlink=1" class="new" title="Talk:Well-founded set (page does not exist)"> </a></li> <li><a href="/wiki/Well-order" title="Well-order">Well-order</a> <a href="/wiki/Talk:Well-order" title="Talk:Well-order"> </a></li></ul></li> <li><a href="/wiki/Power_set" title="Power set">Power set</a> <a href="/wiki/Talk:Power_set" title="Talk:Power set"> </a></li> <li><a href="/wiki/Russell%27s_paradox" title="Russell's paradox">Russell's paradox</a> <a href="/wiki/Talk:Russell%27s_paradox" title="Talk:Russell's paradox"> </a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a> <a href="/wiki/Talk:Set_theory" title="Talk:Set theory"> </a> <ul><li><a href="/wiki/Alternative_set_theory" class="mw-redirect" title="Alternative set theory">Alternative set theory</a> <a href="/wiki/Talk:Alternative_set_theory" class="mw-redirect" title="Talk:Alternative set theory"> </a></li> <li><a href="/wiki/Axiomatic_set_theory" class="mw-redirect" title="Axiomatic set theory">Axiomatic set theory</a> <a href="/wiki/Talk:Axiomatic_set_theory" title="Talk:Axiomatic set theory"> </a></li> <li><a href="/wiki/Kripke%E2%80%93Platek_set_theory_with_urelements" title="Kripke–Platek set theory with urelements">Kripke–Platek set theory with urelements</a> <a href="/wiki/Talk:Kripke%E2%80%93Platek_set_theory_with_urelements" title="Talk:Kripke–Platek set theory with urelements"> </a></li> <li><a href="/wiki/Morse%E2%80%93Kelley_set_theory" title="Morse–Kelley set theory">Morse–Kelley set theory</a> <a href="/wiki/Talk:Morse%E2%80%93Kelley_set_theory" title="Talk:Morse–Kelley set theory"> </a></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive set theory</a> <a href="/wiki/Talk:Naive_set_theory" title="Talk:Naive set theory"> </a></li> <li><a href="/wiki/New_Foundations" title="New Foundations">New Foundations</a> <a href="/wiki/Talk:New_Foundations" title="Talk:New Foundations"> </a></li> <li><a href="/wiki/Positive_set_theory" title="Positive set theory">Positive set theory</a> <a href="/wiki/Talk:Positive_set_theory" title="Talk:Positive set theory"> </a></li> <li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Zermelo–Fraenkel set theory</a> <a href="/wiki/Talk:Zermelo%E2%80%93Fraenkel_set_theory" title="Talk:Zermelo–Fraenkel set theory"> </a></li> <li><a href="/wiki/Zermelo_set_theory" title="Zermelo set theory">Zermelo set theory</a> <a href="/wiki/Talk:Zermelo_set_theory" title="Talk:Zermelo set theory"> </a></li></ul></li> <li><a href="/wiki/Set_(mathematics)" title="Set (mathematics)">Set (mathematics)</a> <a href="/wiki/Talk:Set_(mathematics)" title="Talk:Set (mathematics)"> </a></li> <li><a href="/wiki/Simple_theorems_in_the_algebra_of_sets" title="Simple theorems in the algebra of sets">Simple theorems in the algebra of sets</a> <a href="/wiki/Talk:Simple_theorems_in_the_algebra_of_sets" title="Talk:Simple theorems in the algebra of sets"> </a></li> <li><a href="/wiki/Subset" title="Subset">Subset</a> <a href="/wiki/Talk:Subset" title="Talk:Subset"> </a></li> <li><a href="/wiki/%CE%98_(set_theory)" title="Θ (set theory)">Θ (set theory)</a> <a href="/wiki/Talk:%CE%98_(set_theory)" title="Talk:Θ (set theory)"> </a></li> <li><a href="/wiki/Tree_(descriptive_set_theory)" title="Tree (descriptive set theory)">Tree (descriptive set theory)</a> <a href="/wiki/Talk:Tree_(descriptive_set_theory)" title="Talk:Tree (descriptive set theory)"> </a></li> <li><a href="/wiki/Tree_(set_theory)" title="Tree (set theory)">Tree (set theory)</a> <a href="/wiki/Talk:Tree_(set_theory)" title="Talk:Tree (set theory)"> </a></li> <li><a href="/wiki/Union_(set_theory)" title="Union (set theory)">Union (set theory)</a> <a href="/wiki/Talk:Union_(set_theory)" title="Talk:Union (set theory)"> </a></li> <li><a href="/wiki/Von_Neumann_universe" title="Von Neumann universe">Von Neumann universe</a> <a href="/wiki/Talk:Von_Neumann_universe" title="Talk:Von Neumann universe"> </a></li> <li><a href="/wiki/Zero_sharp" title="Zero sharp">Zero sharp</a> <a href="/wiki/Talk:Zero_sharp" title="Talk:Zero sharp"> </a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Descriptive_set_theory">Descriptive set theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=4" title="Edit section: Descriptive set theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Analytical_hierarchy" title="Analytical hierarchy">Analytical hierarchy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Large_cardinals">Large cardinals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=5" title="Edit section: Large cardinals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Almost_Ramsey_cardinal" class="mw-redirect" title="Almost Ramsey cardinal">Almost Ramsey cardinal</a></li> <li><a href="/wiki/Erd%C5%91s_cardinal" title="Erdős cardinal">Erdős cardinal</a></li> <li><a href="/wiki/Extendible_cardinal" title="Extendible cardinal">Extendible cardinal</a></li> <li><a href="/wiki/Huge_cardinal" title="Huge cardinal">Huge cardinal</a></li> <li><a href="/wiki/Hyper-Woodin_cardinal" class="mw-redirect" title="Hyper-Woodin cardinal">Hyper-Woodin cardinal</a></li> <li><a href="/wiki/Inaccessible_cardinal" title="Inaccessible cardinal">Inaccessible cardinal</a></li> <li><a href="/wiki/Ineffable_cardinal" title="Ineffable cardinal">Ineffable cardinal</a></li> <li><a href="/wiki/Mahlo_cardinal" title="Mahlo cardinal">Mahlo cardinal</a></li> <li><a href="/wiki/Measurable_cardinal" title="Measurable cardinal">Measurable cardinal</a></li> <li><a href="/wiki/N-huge_cardinal" class="mw-redirect" title="N-huge cardinal">N-huge cardinal</a></li> <li><a href="/wiki/Ramsey_cardinal" title="Ramsey cardinal">Ramsey cardinal</a></li> <li><a href="/wiki/Rank-into-rank" title="Rank-into-rank">Rank-into-rank</a></li> <li><a href="/wiki/Remarkable_cardinal" title="Remarkable cardinal">Remarkable cardinal</a></li> <li><a href="/wiki/Shelah_cardinal" title="Shelah cardinal">Shelah cardinal</a></li> <li><a href="/wiki/Strong_cardinal" title="Strong cardinal">Strong cardinal</a></li> <li><a href="/wiki/Strongly_inaccessible_cardinal" class="mw-redirect" title="Strongly inaccessible cardinal">Strongly inaccessible cardinal</a></li> <li><a href="/wiki/Subtle_cardinal" title="Subtle cardinal">Subtle cardinal</a></li> <li><a href="/wiki/Supercompact_cardinal" title="Supercompact cardinal">Supercompact cardinal</a></li> <li><a href="/wiki/Superstrong_cardinal" title="Superstrong cardinal">Superstrong cardinal</a></li> <li><a href="/wiki/Totally_indescribable_cardinal" class="mw-redirect" title="Totally indescribable cardinal">Totally indescribable cardinal</a></li> <li><a href="/wiki/Weakly_compact_cardinal" title="Weakly compact cardinal">Weakly compact cardinal</a></li> <li><a href="/wiki/Weakly_hyper-Woodin_cardinal" class="mw-redirect" title="Weakly hyper-Woodin cardinal">Weakly hyper-Woodin cardinal</a></li> <li><a href="/wiki/Weakly_inaccessible_cardinal" class="mw-redirect" title="Weakly inaccessible cardinal">Weakly inaccessible cardinal</a></li> <li><a href="/wiki/Woodin_cardinal" title="Woodin cardinal">Woodin cardinal</a></li> <li><a href="/wiki/Unfoldable_cardinal" title="Unfoldable cardinal">Unfoldable cardinal</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Recursion_theory">Recursion theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=6" title="Edit section: Recursion theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Entscheidungsproblem" title="Entscheidungsproblem">Entscheidungsproblem</a></li> <li><a href="/wiki/Decision_problem" title="Decision problem">Decision problem</a></li> <li><a href="/wiki/Decidability_(logic)" title="Decidability (logic)">Decidability (logic)</a></li> <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> <ul><li><a href="/wiki/Algorithm" title="Algorithm">Algorithm</a></li> <li><a href="/wiki/Recursion" title="Recursion">Recursion</a></li> <li><a href="/wiki/Primitive_recursive_function" title="Primitive recursive function">Primitive recursive function</a></li> <li><a href="/wiki/Mu_operator" class="mw-redirect" title="Mu operator">Mu operator</a></li> <li><a href="/wiki/Ackermann_function" title="Ackermann function">Ackermann function</a></li> <li><a href="/wiki/Turing_machine" title="Turing machine">Turing machine</a></li> <li><a href="/wiki/Halting_problem" title="Halting problem">Halting problem</a></li> <li><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a>, <a href="/wiki/Computation" title="Computation">computation</a></li> <li><a href="/wiki/Herbrand_Universe" class="mw-redirect" title="Herbrand Universe">Herbrand Universe</a></li> <li><a href="/wiki/Markov_algorithm" title="Markov algorithm">Markov algorithm</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a> <ul><li><a href="/wiki/Church-Rosser_theorem" class="mw-redirect" title="Church-Rosser theorem">Church-Rosser theorem</a></li> <li><a href="/wiki/Calculus_of_constructions" title="Calculus of constructions">Calculus of constructions</a></li></ul></li> <li><a href="/wiki/Combinatory_logic" title="Combinatory logic">Combinatory logic</a></li> <li><a href="/wiki/Post_correspondence_problem" title="Post correspondence problem">Post correspondence problem</a></li></ul></li> <li><a href="/wiki/Kleene%27s_recursion_theorem" title="Kleene's recursion theorem">Kleene's recursion theorem</a></li> <li><a href="/wiki/Recursively_enumerable_set" class="mw-redirect" title="Recursively enumerable set">Recursively enumerable set</a> <ul><li><a href="/wiki/Recursively_enumerable_language" title="Recursively enumerable language">Recursively enumerable language</a></li></ul></li> <li><a href="/wiki/Decidable_language" class="mw-redirect" title="Decidable language">Decidable language</a></li> <li><a href="/wiki/Undecidable_language" class="mw-redirect" title="Undecidable language">Undecidable language</a></li> <li><a href="/wiki/Rice%27s_theorem" title="Rice's theorem">Rice's theorem</a></li> <li><a href="/wiki/Post%27s_theorem" title="Post's theorem">Post's theorem</a></li> <li><a href="/wiki/Turing_degree" title="Turing degree">Turing degree</a></li> <li><a href="/wiki/Effective_results_in_number_theory" title="Effective results in number theory">Effective results in number theory</a></li> <li><a href="/wiki/Diophantine_set" title="Diophantine set">Diophantine set</a></li> <li><a href="/wiki/Matiyasevich%27s_theorem" class="mw-redirect" title="Matiyasevich's theorem">Matiyasevich's theorem</a></li> <li><a href="/wiki/Word_problem_for_groups" title="Word problem for groups">Word problem for groups</a></li> <li><a href="/wiki/Arithmetical_hierarchy" title="Arithmetical hierarchy">Arithmetical hierarchy</a></li> <li><a href="/w/index.php?title=Subrecursion_theory&action=edit&redlink=1" class="new" title="Subrecursion theory (page does not exist)">Subrecursion theory</a> <ul><li><a href="/wiki/Presburger_arithmetic" title="Presburger arithmetic">Presburger arithmetic</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Polynomial_time" class="mw-redirect" title="Polynomial time">Polynomial time</a></li> <li><a href="/wiki/Exponential_time" class="mw-redirect" title="Exponential time">Exponential time</a></li> <li><a href="/wiki/Complexity_class" title="Complexity class">Complexity class</a> <ul><li><a href="/wiki/P_%3D_NP_problem" class="mw-redirect" title="P = NP problem">Complexity classes P and NP</a></li> <li><a href="/wiki/Cook%27s_theorem" class="mw-redirect" title="Cook's theorem">Cook's theorem</a></li> <li><a href="/wiki/List_of_complexity_classes" title="List of complexity classes">List of complexity classes</a></li> <li><a href="/wiki/Polynomial_hierarchy" title="Polynomial hierarchy">Polynomial hierarchy</a></li> <li><a href="/wiki/Exponential_hierarchy" title="Exponential hierarchy">Exponential hierarchy</a></li></ul></li> <li><a href="/wiki/NP-complete" class="mw-redirect" title="NP-complete">NP-complete</a></li> <li><a href="/wiki/Time_hierarchy_theorem" title="Time hierarchy theorem">Time hierarchy theorem</a></li> <li><a href="/wiki/Space_hierarchy_theorem" title="Space hierarchy theorem">Space hierarchy theorem</a></li></ul></li> <li><a href="/wiki/Natural_proof" title="Natural proof">Natural proof</a></li> <li><a href="/wiki/Hypercomputation" title="Hypercomputation">Hypercomputation</a> <ul><li><a href="/wiki/Oracle_machine" title="Oracle machine">Oracle machine</a></li></ul></li> <li><a href="/wiki/R%C3%B3zsa_P%C3%A9ter" title="Rózsa Péter">Rózsa Péter</a></li> <li><a href="/wiki/Alonzo_Church" title="Alonzo Church">Alonzo Church</a></li> <li><a href="/wiki/Emil_Post" class="mw-redirect" title="Emil Post">Emil Post</a></li> <li><a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a></li> <li><a href="/wiki/Jacques_Herbrand" title="Jacques Herbrand">Jacques Herbrand</a></li> <li><a href="/wiki/Haskell_Curry" title="Haskell Curry">Haskell Curry</a></li> <li><a href="/wiki/Stephen_Cole_Kleene" title="Stephen Cole Kleene">Stephen Cole Kleene</a></li> <li><a href="/wiki/Definable_real_number" title="Definable real number">Definable real number</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Proof_theory">Proof theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=7" title="Edit section: Proof theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Metamathematics" title="Metamathematics">Metamathematics</a></li> <li><a href="/wiki/Cut-elimination" class="mw-redirect" title="Cut-elimination">Cut-elimination</a></li> <li><a href="/wiki/Tarski%27s_undefinability_theorem" title="Tarski's undefinability theorem">Tarski's undefinability theorem</a></li> <li><a href="/wiki/Diagonal_lemma" title="Diagonal lemma">Diagonal lemma</a></li> <li><a href="/wiki/Provability_logic" title="Provability logic">Provability logic</a></li> <li><a href="/wiki/Interpretability_logic" title="Interpretability logic">Interpretability logic</a></li> <li><a href="/wiki/Sequent" title="Sequent">Sequent</a></li> <li><a href="/wiki/Sequent_calculus" title="Sequent calculus">Sequent calculus</a></li> <li><a href="/wiki/Analytic_proof" title="Analytic proof">Analytic proof</a></li> <li><a href="/wiki/Structural_proof_theory" title="Structural proof theory">Structural proof theory</a></li> <li><a href="/wiki/Self-verifying_theories" title="Self-verifying theories">Self-verifying theories</a></li> <li><a href="/wiki/Substructural_logic" title="Substructural logic">Substructural logics</a> <ul><li><a href="/wiki/Structural_rule" title="Structural rule">Structural rule</a> <ul><li><a href="/wiki/Weakening_(logic)" class="mw-redirect" title="Weakening (logic)">Weakening</a></li> <li><a href="/wiki/Contraction_(logic)" class="mw-redirect" title="Contraction (logic)">Contraction</a></li></ul></li> <li><a href="/wiki/Linear_logic" title="Linear logic">Linear logic</a> <ul><li><a href="/wiki/Intuitionistic_linear_logic" class="mw-redirect" title="Intuitionistic linear logic">Intuitionistic linear logic</a></li> <li><a href="/wiki/Proof_net" title="Proof net">Proof net</a></li></ul></li> <li><a href="/wiki/Affine_logic" title="Affine logic">Affine logic</a></li> <li><a href="/w/index.php?title=Strict_logic&action=edit&redlink=1" class="new" title="Strict logic (page does not exist)">Strict logic</a></li> <li><a href="/wiki/Relevant_logic" class="mw-redirect" title="Relevant logic">Relevant logic</a></li></ul></li> <li><a href="/wiki/Proof-theoretic_semantics" title="Proof-theoretic semantics">Proof-theoretic semantics</a></li> <li><a href="/wiki/Ludics" title="Ludics">Ludics</a></li> <li><a href="/wiki/System_F" title="System F">System F</a></li> <li><a href="/wiki/Gerhard_Gentzen" title="Gerhard Gentzen">Gerhard Gentzen</a></li> <li><a href="/wiki/Gentzen%27s_consistency_proof" title="Gentzen's consistency proof">Gentzen's consistency proof</a></li> <li><a href="/wiki/Reverse_mathematics" title="Reverse mathematics">Reverse mathematics</a></li> <li><a href="/wiki/Nonfirstorderizability" title="Nonfirstorderizability">Nonfirstorderizability</a></li> <li><a href="/wiki/Interpretability" title="Interpretability">Interpretability</a></li> <li><a href="/wiki/Weak_interpretability" title="Weak interpretability">Weak interpretability</a></li> <li><a href="/wiki/Cointerpretability" title="Cointerpretability">Cointerpretability</a></li> <li><a href="/wiki/Tolerant_sequence" title="Tolerant sequence">Tolerant sequence</a></li> <li><a href="/w/index.php?title=Cotolerant_sequence&action=edit&redlink=1" class="new" title="Cotolerant sequence (page does not exist)">Cotolerant sequence</a></li> <li><a href="/wiki/Deduction_theorem" title="Deduction theorem">Deduction theorem</a></li> <li><a href="/wiki/Cirquent_calculus" title="Cirquent calculus">Cirquent calculus</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Mathematical_constructivism">Mathematical constructivism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=8" title="Edit section: Mathematical constructivism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Nonconstructive_proof" class="mw-redirect" title="Nonconstructive proof">Nonconstructive proof</a></li> <li><a href="/wiki/Existence_theorem" title="Existence theorem">Existence theorem</a></li> <li><a href="/wiki/Intuitionistic_logic" title="Intuitionistic logic">Intuitionistic logic</a></li> <li><a href="/wiki/Intuitionistic_type_theory" title="Intuitionistic type theory">Intuitionistic type theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a> <ul><li><a href="/wiki/Church%E2%80%93Rosser_theorem" title="Church–Rosser theorem">Church–Rosser theorem</a></li></ul></li> <li><a href="/wiki/Simply_typed_lambda_calculus" title="Simply typed lambda calculus">Simply typed lambda calculus</a></li> <li><a href="/wiki/Typed_lambda_calculus" title="Typed lambda calculus">Typed lambda calculus</a></li> <li><a href="/wiki/Curry%E2%80%93Howard_isomorphism" class="mw-redirect" title="Curry–Howard isomorphism">Curry–Howard isomorphism</a></li> <li><a href="/wiki/Calculus_of_constructions" title="Calculus of constructions">Calculus of constructions</a></li> <li><a href="/wiki/Constructivist_analysis" class="mw-redirect" title="Constructivist analysis">Constructivist analysis</a></li> <li><a href="/wiki/Lambda_cube" title="Lambda cube">Lambda cube</a></li> <li><a href="/wiki/System_F" title="System F">System F</a></li> <li><a href="/wiki/Introduction_to_topos_theory" class="mw-redirect" title="Introduction to topos theory">Introduction to topos theory</a></li> <li><a href="/wiki/LF_(logical_framework)" class="mw-redirect" title="LF (logical framework)">LF (logical framework)</a></li> <li><a href="/wiki/Computability_logic" title="Computability logic">Computability logic</a></li> <li><a href="/wiki/Computable_measure_theory" title="Computable measure theory">Computable measure theory</a></li> <li><a href="/wiki/Finitism" title="Finitism">Finitism</a></li> <li><a href="/wiki/Ultraintuitionism" class="mw-redirect" title="Ultraintuitionism">Ultraintuitionism</a></li> <li><a href="/wiki/Luitzen_Egbertus_Jan_Brouwer" class="mw-redirect" title="Luitzen Egbertus Jan Brouwer">Luitzen Egbertus Jan Brouwer</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Modal_logic">Modal logic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=9" title="Edit section: Modal logic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kripke_semantics" title="Kripke semantics">Kripke semantics</a></li> <li><a href="/wiki/Sahlqvist_formula" title="Sahlqvist formula">Sahlqvist formula</a></li> <li><a href="/wiki/Interior_algebra" title="Interior algebra">Interior algebra</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Theorem_provers">Theorem provers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_mathematical_logic_topics&action=edit&section=10" title="Edit section: Theorem provers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/First-order_resolution" class="mw-redirect" title="First-order resolution">First-order resolution</a></li> <li><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Automated theorem proving</a></li> <li><a href="/wiki/ACL2_theorem_prover" class="mw-redirect" title="ACL2 theorem prover">ACL2 theorem prover</a></li> <li><a href="/wiki/E_equational_theorem_prover" class="mw-redirect" title="E equational theorem prover">E equational theorem prover</a></li> <li><a href="/w/index.php?title=Gandalf_theorem_prover&action=edit&redlink=1" class="new" title="Gandalf theorem prover (page does not exist)">Gandalf theorem prover</a></li> <li><a href="/wiki/HOL_theorem_prover" class="mw-redirect" title="HOL theorem prover">HOL theorem prover</a></li> <li><a href="/wiki/Isabelle_theorem_prover" class="mw-redirect" title="Isabelle theorem prover">Isabelle theorem prover</a></li> <li><a href="/wiki/LCF_theorem_prover" class="mw-redirect" title="LCF theorem prover">LCF theorem prover</a></li> <li><a href="/wiki/Otter_theorem_prover" 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title="Logic">Logic</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_logic" title="Outline of logic">Outline</a></li> <li><a href="/wiki/History_of_logic" title="History of logic">History</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major fields</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/Logic_in_computer_science" title="Logic in computer science">Computer science</a></li> <li><a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Philosophy_of_logic" title="Philosophy of logic">Philosophy of logic</a></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Syntax_(logic)" title="Syntax (logic)">Syntax</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Logics</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/Classical_logic" title="Classical logic">Classical</a></li> <li><a href="/wiki/Informal_logic" title="Informal logic">Informal</a> <ul><li><a href="/wiki/Critical_thinking" title="Critical thinking">Critical thinking</a></li> <li><a href="/wiki/Reason" title="Reason">Reason</a></li></ul></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical</a></li> <li><a href="/wiki/Non-classical_logic" title="Non-classical logic">Non-classical</a></li> <li><a href="/wiki/Philosophical_logic" title="Philosophical logic">Philosophical</a></li></ul> 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href="/wiki/Inductive_reasoning" title="Inductive reasoning">Induction</a></li> <li><a href="/wiki/Logical_truth" title="Logical truth">Logical truth</a></li> <li><a href="/wiki/Name" title="Name">Name</a></li> <li><a href="/wiki/Necessity_and_sufficiency" title="Necessity and sufficiency">Necessity and sufficiency</a></li> <li><a href="/wiki/Premise" title="Premise">Premise</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Reference" title="Reference">Reference</a></li> <li><a href="/wiki/Statement_(logic)" title="Statement (logic)">Statement</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Truth" title="Truth">Truth</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" 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style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_logicians" title="List of logicians">Logicians</a></li> <li><a href="/wiki/List_of_rules_of_inference" title="List of rules of inference">Rules of inference</a></li> <li><a href="/wiki/List_of_paradoxes" title="List of paradoxes">Paradoxes</a></li> <li><a href="/wiki/List_of_fallacies" title="List of fallacies">Fallacies</a></li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">Logic symbols</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, 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