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
21 pages build on this one.
- Ryll-Nardzewski theorem
- Ehrenfeucht–Fraïssé game
- Well-formed formula
- Amalgamation property
- Dense linear order
- Löwenheim–Skolem theorem
- Term
- Stable theory
- Craig interpolation theorem
- Skolem normal form
- Lindström's theorem
- Theory
- Substructure
- Quantifier elimination
- Beth definability theorem
- Robinson arithmetic
- Type
- Ultraproduct
- Herbrand's theorem
- Structure
- Łoś–Vaught test
Further reading
About this page
| Tag | WDVVEYD6AT |
|---|---|
| URI | m2://WDVVEYD6AT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07, 03B10 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Ehrenfeucht–Fraïssé game
- Well-formed formula
- Amalgamation property
- Löwenheim–Skolem theorem
- Term
- Craig interpolation theorem
- Skolem normal form
- Theory
- Substructure
- Quantifier elimination
- Robinson arithmetic
- Type
- Ultraproduct
- Herbrand's theorem
- Structure