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First-order logic
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Mathematical logic
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Words: 806
Articles: 27
First-order logic permits quantification over elements of a structure while its nonlogical symbols describe operations, constants, and relations.
Table of contents
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
(5)
Mathematical logic
Foundations of mathematics
Area of mathematics
Mathematics
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