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Mathematical logic
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Foundations of mathematics
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Words: 1k
Articles: 37
Mathematical logic studies formal languages, proofs, models, computability, and the foundations of mathematics.
Table of contents
1k
37
Propositional logic
Mathematical logic
236
8
Soundness theorem for propositional logic
Propositional logic
16
Deductively closed set of formulae
Propositional logic
19
Consistent set of formulae
Propositional logic
25
Finitary set of formulae
Propositional logic
23
Increasing union of deductively closed sets
Propositional logic
31
Maximal consistent set in propositional logic
Propositional logic
44
Propositional compactness theorem
Propositional logic
78
1
Compactness obstruction to expressing totality over an infinite codomain
Propositional compactness theorem
46
First-order logic
Mathematical logic
806
27
First-order language
First-order logic
47
1
Finite language support
First-order language
29
Free variable
First-order logic
19
First-order sentence
First-order logic
22
First-order theory
First-order logic
177
6
First-order axiomatizable class
First-order theory
41
Consistent first-order theory
First-order theory
38
1
Monotonicity of inconsistency
Consistent first-order theory
17
Finite character of formal proofs
First-order theory
17
Universal first-order theory
First-order theory
58
1
Finite forbidden-pattern axiomatization
Universal first-order theory
38
First-order structure
First-order logic
207
6
Model of a first-order theory
First-order structure
16
Automorphism of a first-order structure
First-order structure
172
4
First-order axiomatization of an automorphism
Automorphism of a first-order structure
33
Faithful automorphism action
Automorphism of a first-order structure
30
Rigid first-order structure
Automorphism of a first-order structure
90
1
Compactness transfer of finite nonrigidity
Rigid first-order structure
59
Soundness theorem for first-order logic
First-order logic
15
Godel completeness theorem
First-order logic
24
Compactness theorem
First-order logic
144
3
Syntactic proof of first-order compactness
Compactness theorem
32
Compactness obstruction to axiomatizing finitely many maximal elements
Compactness theorem
41
Compactness obstruction to an exclusive disjunction of infinitude
Compactness theorem
53
Lowenheim-Skolem theorem
First-order logic
133
2
Upward Lowenheim-Skolem theorem
Lowenheim-Skolem theorem
65
Downward Lowenheim-Skolem theorem
Lowenheim-Skolem theorem
51
Ancestors
(4)
Foundations of mathematics
Area of mathematics
Mathematics
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