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Template:Mathematical logic: Difference between revisions

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   | list0 =
   | list0 =
* [[Axiom]]
* [[Axiom]]
** [[List of axioms|list]]
* [[Cardinality]]
* [[First-order logic]]
* [[First-order logic]]
* [[Formal proof]]
* [[Formal proof]]
* [[Logical consequence]]
* [[Formal semantics (logic)|Formal semantics]]
* [[Formal semantics (logic)|Formal semantics]]
* [[Foundations of mathematics]]
* [[Foundations of mathematics]]
* [[Information theory]]
* [[Logical consequence]]
* [[Structure (mathematical logic)|Model]]
* [[Structure (mathematical logic)|Model]]
* [[Set (mathematics)|Set]]
* [[Set (mathematics)|Set]]
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* [[Type theory]]
* [[Type theory]]


   | group10 = Theorems&nbsp;([[:Category:Theorems in the foundations of mathematics|list]])
   | group10 = Theorems&nbsp;([[:Category:Theorems in the foundations of mathematics|list]])<br />&nbsp;&amp;&nbsp;[[Paradoxes of set theory|Paradoxes]]
   | list10 =  
   | list10 =  
* [[Gödel's completeness theorem|Gödel's completeness]]&nbsp;and&nbsp;[[Gödel's incompleteness theorems|incompleteness theorems]]
* {{nowrap|[[Gödel's completeness theorem|Gödel's completeness]]&nbsp;and&nbsp;[[Gödel's incompleteness theorems|incompleteness theorems]]}}
* [[Tarski's undefinability theorem|Tarski's undefinability]]
* [[Tarski's undefinability theorem|Tarski's undefinability]]
* [[Banach–Tarski paradox]]
* [[Banach–Tarski paradox]]
* Cantor's&nbsp;[[Cantor's theorem|theorem,]]&nbsp;[[Cantor's paradox|paradox]]&nbsp;and&nbsp;[[Cantor's diagonal argument|diagonal argument]]
* {{nowrap|Cantor's&nbsp;[[Cantor's theorem|theorem,]]&nbsp;[[Cantor's paradox|paradox]]&nbsp;and&nbsp;[[Cantor's diagonal argument|diagonal argument]]}}
* [[Compactness theorem|Compactness]]
* [[Halting problem]]
* [[Lindström's theorem|Lindström's]]
* [[Lindström's theorem|Lindström's]]
* [[Löwenheim–Skolem theorem|Löwenheim–Skolem]]
* [[Löwenheim–Skolem theorem|Löwenheim–Skolem]]
* [[Compactness theorem|Compactness]]
* [[Russell's paradox]]


   | group20 = [[Logic]]s
   | group20 = [[Logic]]s
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   | list1  =
   | list1  =
* [[Classical logic]]
* [[Classical logic]]
* [[Logical truth]]
* [[Tautology (logic)|Tautology]]
* [[Proposition]]
* [[Proposition]]
* [[Inference]]
* [[Inference]]
* [[Logical equivalence]]
* [[Logical equivalence]]
* [[Consistency]]
** [[Equiconsistency]]
* [[Argument]]
* [[Argument]]
* [[Soundness]]
* [[Validity (logic)|Validity]]
* [[Validity (logic)|Validity]]
* [[Syllogism]]
* [[Syllogism]]
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* [[Truth table]]s
* [[Truth table]]s
* [[Many-valued logic]]
* [[Many-valued logic]]
** [[Three-valued logic|3]]
** [[Finite-valued logic|Finite]]
** [[Infinite-valued logic|∞]]


   | group4 = [[Predicate logic|Predicate]]
   | group4 = [[Predicate logic|Predicate]]
   | list4 =
   | list4 =
* [[First-order logic|First-order]]
* [[First-order logic|First-order]]
* [[Second-order logic|Second-order]]
** [[Monadic second-order logic|Monadic]]
* [[Higher-order logic|Higher-order]]
* [[Free logic|Free]]
* [[Quantifier (logic)|Quantifiers]]
* [[Quantifier (logic)|Quantifiers]]
* [[Predicate (mathematical logic)|Predicate]]
* [[Predicate (mathematical logic)|Predicate]]
* [[Second-order logic|Second-order]]
* [[Monadic predicate calculus]]
* [[Monadic predicate calculus]]
}}<!--END:{{Navbox|subgroup-->
}}<!--END:{{Navbox|subgroup-->
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   | list1  =
   | list1  =
* [[Set (mathematics)|Set]]
* [[Set (mathematics)|Set]]
* [[Element (mathematics)|Element]]
** [[Hereditary set|Hereditary]]
* [[Class (set theory)|Class]]
* ([[Urelement|Ur-]])[[Element (mathematics)|Element]]
* [[Ordered pair]]
* [[Ordered pair]]
* [[Ordinal number]]
* [[Ordinal number]]
* [[Russell's paradox]]
* [[Power set]]
* [[Subset]]
* [[Subset]]
* [[Binary operation|Relation]]
* [[Equality (mathematics)|Equality]]
* [[Extensionality]]
* [[Forcing (mathematics)|Forcing]]
* [[Relation (mathematics)|Relation]]
** [[Equivalence relation|Equivalence]]
** [[Partition of a set|Partition]]
* Set operations:
** [[Intersection (set theory)|Intersection]]
** [[Union (set theory)|Union]]
** [[Complement (set theory)|Complement]]
** [[Cartesian product]]
** [[Power set]]
** [[List of set identities and relations|Identities]]
 
  | group3 = Types of [[Set (mathematics)|Set]]s
  | list3  =
* [[Countable set|Countable]]
* [[Uncountable set|Uncountable]]
* [[Empty set|Empty]]
* [[Inhabited set|Inhabited]]
* [[Singleton (mathematics)|Singleton]]
* [[Finite set|Finite]]
* [[Infinite set|Infinite]]
* [[Transitive set|Transitive]]
* [[Ultrafilter (set theory)|Ultrafilter]]
* [[Recursive set|Recursive]]
* [[Fuzzy set|Fuzzy]]
* [[Universal set|Universal]]
* [[Universe (mathematics)|Universe]]
** [[Constructible universe|Constructible]]
** [[Grothendieck universe|Grothendieck]]
** [[Von Neumann universe|Von Neumann]]
  | group5 = [[Map (mathematics)|Map]]s&nbsp;&amp;&nbsp;[[Cardinality]]
  | list5  =
* [[Function (mathematics)|Function]]/[[Map (mathematics)|Map]]
* [[Function (mathematics)|Function]]/[[Map (mathematics)|Map]]
** [[Domain of a function|Domain]]
** [[Domain of a function|Domain]]
** [[Codomain]]
** [[Codomain]]
** [[Image (mathematics)|Image]]
** [[Image (mathematics)|Image]]
* [[Extensionality]]
* [[Injective function|In]]/[[Surjective function|Sur]]/[[Bijection|Bi]]-jection
* [[Forcing (mathematics)|Forcing]]
* [[Schröder–Bernstein theorem]]
 
* [[Isomorphism]]
  | group2 = [[Cardinality]]
* [[Gödel numbering]]
  | list2  =
* [[Empty set]]
* [[Inhabited set]]
* [[Enumeration]]
* [[Enumeration]]
* [[Countable set]]
* [[Large cardinal]]
* [[Uncountable set]]
** [[Inaccessible cardinal|Inaccessible]]
* [[Finite set]]
* [[Aleph number]]
* [[Infinite set]]
* [[Operation (mathematics)|Operation]]
* [[Class (set theory)|Class]]
** [[Binary operation|Binary]]
* [[Schröder–Bernstein theorem]]


   | group7 = Set theories
   | group8 = Set theories
   | list7 =
   | list8 =
* [[Zermelo–Fraenkel set theory|Zermelo–Fraenkel]]
* [[Zermelo–Fraenkel set theory|Zermelo–Fraenkel]]
** [[Axiom of choice]]
** [[Axiom of choice]]
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* [[Morse–Kelley set theory|Morse–Kelley]]
* [[Morse–Kelley set theory|Morse–Kelley]]
* [[Naive set theory|Naive]]
* [[Naive set theory|Naive]]
* [[New Foundations]]
* [[Tarski–Grothendieck set theory|Tarski–Grothendieck]]
* [[Tarski–Grothendieck set theory|Tarski–Grothendieck]]
* [[Von Neumann–Bernays–Gödel set theory|Von Neumann–Bernays–Gödel]]
* [[Von Neumann–Bernays–Gödel set theory|Von Neumann–Bernays–Gödel]]
* [[Constructive set theory|Constructive]]
}}
}}


   | group70 = [[Syntax (logic)|Syntax]]&nbsp;&amp;&nbsp;[[Formal language|Language]]
   | group70 = [[Syntax (logic)|Syntax]]&nbsp;&amp;&nbsp;[[Formal language|Language]]
   | list70 =
   | list70 =
  {{Navbox|subgroup
  | group1 =
  | list1  =
* [[Alphabet (formal languages)|Alphabet]]
* [[Alphabet (formal languages)|Alphabet]]
* [[Arity]]
* [[Arity]]
* [[Automata theory|Automata]]
* [[Axiom schema]]
* [[Expression (mathematics)|Expression]]
* [[Expression (mathematics)|Expression]]
** [[Ground expression|Ground]]
** [[Ground expression|Ground]]
* [[Extension by new constant and function names|Extension]]
* [[Extension by new constant and function names|Extension]]
** [[Extension by definitions|by definition]]
** [[Conservative extension|Conservative]]
* [[Finitary relation|Relation]]
* [[Finitary relation|Relation]]
* Formal
* Formal
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** [[Open formula|Open]]
** [[Open formula|Open]]
* [[Free variables and bound variables|Free/bound variable]]
* [[Free variables and bound variables|Free/bound variable]]
* [[Metalanguage]]
* [[Logical connective]]
* [[Logical connective]]
** [[Negation|¬]]
** [[Negation|¬]]
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* [[Quantifier (logic)|Quantifier]]
* [[Quantifier (logic)|Quantifier]]
** [[Existential quantification|∃]]
** [[Existential quantification|∃]]
** [[Uniqueness quantification|!]]
** [[Universal quantification|∀]]
** [[Universal quantification|∀]]
** [[Quantifier rank|rank]]
* [[Sentence (mathematical logic)|Sentence]]
* [[Sentence (mathematical logic)|Sentence]]
** [[Atomic sentence|Atomic]]
** [[Atomic sentence|Atomic]]
** [[Spectrum of a sentence|Spectrum]]
* [[Signature (logic)|Signature]]
* [[Signature (logic)|Signature]]
* [[String (formal languages)|String]]
* [[String (formal languages)|String]]
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** [[Variable (mathematics)|Variable]]
** [[Variable (mathematics)|Variable]]
* [[Term (logic)|Term]]
* [[Term (logic)|Term]]
  | group8 = {{nowarp|Example&nbsp;[[Axiomatic system|axiomatic<br/>systems]]&nbsp;{{smaller|([[List of first-order theories|list]])}}}}
  | list8 =
* of [[True arithmetic|arithmetic]]:
** [[Peano axioms|Peano]]
** [[Second-order arithmetic|second-order]]
** [[Elementary function arithmetic|elementary function]]
** [[Primitive recursive arithmetic|primitive recursive]]
** [[Robinson arithmetic|Robinson]]
** [[Skolem arithmetic|Skolem]]
* of the [[Construction of the real numbers|real numbers]]
** [[Tarski's axiomatization of the reals|Tarski's axiomatization]]
* of [[Axiomatization of Boolean algebras|Boolean algebras]]
** [[Boolean algebras canonically defined|canonical]]
** [[Minimal axioms for Boolean algebra|minimal axioms]]
* of [[Foundations of geometry|geometry]]:
** [[Euclidean geometry|Euclidean]]
** [[Euclid's Elements|''Elements'']]
** [[Hilbert's axioms|Hilbert's]]
** [[Non-Euclidean geometry|non-Euclidean]]
** [[Tarski's axioms|Tarski's]]
* ''[[Principia Mathematica]]''
}}<!--END:{{Navbox|subgroup-->


   | group80 = [[Proof theory]]
   | group80 = [[Proof theory]]
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** [[Deductive system|Deductive]]
** [[Deductive system|Deductive]]
** [[Hilbert system|Hilbert]]
** [[Hilbert system|Hilbert]]
*** [[List of Hilbert systems|list]]
* [[Complete theory]]
* [[Complete theory]]
* [[Independence (mathematical logic)|Independence]]&nbsp;([[List of statements independent of ZFC|from&nbsp;ZFC]])
* [[Independence (mathematical logic)|Independence]]&nbsp;([[List of statements independent of ZFC|from&nbsp;ZFC]])
* [[Proof of impossibility]]
* [[Ordinal analysis]]
* [[Reverse mathematics]]
* [[Self-verifying theories]]


   | group90 = [[Model theory]]
   | group90 = [[Model theory]]
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** [[Finite model theory|Finite]]
** [[Finite model theory|Finite]]
** [[Saturated model|Saturated]]
** [[Saturated model|Saturated]]
** [[Spectrum of a theory|Spectrum]]
** [[Substructure (mathematics)|Substructure]]
** [[Substructure (mathematics)|Substructure]]
* [[Non-standard model]]
* [[Non-standard model]]
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* [[Categorical theory]]
* [[Categorical theory]]
* [[Model complete theory]]
* [[Model complete theory]]
* [[Satisfiability]]
* [[Semantics of logic]]
* [[Strength (mathematical logic)|Strength]]
* [[Strength (mathematical logic)|Strength]]
* [[Semantics of logic]]
* [[Theories of truth]]
* [[Theories of truth]]
** [[Semantic theory of truth|Semantic]]
** [[Semantic theory of truth|Semantic]]
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* [[Validity (logic)|Validity]]
* [[Validity (logic)|Validity]]


   | group100 = [[Computability theory|Computability theory]]
   | group100 = [[Computability theory]]
   | list100 =
   | list100 =
* [[Church encoding]]
* [[Church–Turing thesis]]
* [[Church–Turing thesis]]
* [[Computably enumerable]]
* [[Computably enumerable set|Computably enumerable]]
* [[Computable function]]
* [[Computable function]]
* [[Computable set]]
* [[Computable set]]
* [[Decision problem]]
* [[Decision problem]]
* [[Halting problem]]
** [[Decidability (logic)|Decidable]]
** [[Undecidable problem|Undecidable]]
** [[P (complexity)|P]]
** [[NP (complexity)|NP]]
** [[P versus NP problem]]
* [[Kolmogorov complexity]]
* [[Lambda calculus]]
* [[Primitive recursive function]]
* [[Primitive recursive function]]
* [[Recursion]]
* [[Recursion]]
* [[Recursive set]]
* [[Recursive set]]
* [[Turing machine]]
* [[Type theory]]
 
  | group120 = Related
  | list120 =
* [[Abstract logic]]
* [[Category theory]]
* [[Concrete category|Concrete]]/[[Category (mathematics)|Abstract Category]]
* [[Category of sets]]
* [[History of logic]]
* [[History of mathematical logic]]
** [[Timeline of mathematical logic|timeline]]
* [[Logicism]]
* [[Mathematical object]]
* [[Philosophy of mathematics]]
* [[Supertask]]


<!--| below = ...-->
|below='''{{portal-inline|size=tiny|Mathematics}}'''
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}}<noinclude>
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{{documentation|content=

Revision as of 05:09, 2 November 2022

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