Mathematical logic and foundations First-order logic Concept
Signature
Summary
A signature lists the non-logical symbols of a first-order language: function symbols, relation symbols and constant symbols, each with its number of arguments. It fixes what one can talk about, before any axioms are chosen. Terms, formulas and structures are always taken over a given signature. Another name is vocabulary, and in Mathlib it is called a first-order language.
Where this leads
32 pages build on this one.
- Ryll-Nardzewski theorem
- Ehrenfeucht–Fraïssé game
- Herbrand universe
- Well-formed formula
- Relational structure
- Amalgamation property
- Dense linear order
- Löwenheim–Skolem theorem
- Elementary class
- Algebraic structure
- Term
- Stable theory
- Homomorphism
- Craig interpolation theorem
- Skolem normal form
- Lindström's theorem
- Theory
- Substructure
- Countably generated structure
- Universal class
- Universal Horn class
- Quantifier elimination
- Beth definability theorem
- Robinson arithmetic
- Term algebra
- Term evaluation
- Type
- Ultraproduct
- Herbrand's theorem
- Substitution
- Structure
- Łoś–Vaught test
Further reading
About this page
| Tag | WDVVEYD6AT |
|---|---|
| URI | m2://WDVVEYD6AT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07, 03B10 |
| Same as |
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Used by
- Ehrenfeucht–Fraïssé game
- Well-formed formula
- Relational structure
- Amalgamation property
- Löwenheim–Skolem theorem
- Elementary class
- Algebraic structure
- Term
- Homomorphism
- Craig interpolation theorem
- Skolem normal form
- Theory
- Substructure
- Countably generated structure
- Universal class
- Universal Horn class
- Quantifier elimination
- Robinson arithmetic
- Term algebra
- Term evaluation
- Type
- Ultraproduct
- Herbrand's theorem
- Substitution
- Structure