Mathematical logic and foundations Model theory: basic notions Concept
Structure
Summary
A structure for a signature is a set together with a meaning for each symbol of the signature. Each symbol becomes a function, a relation or an element of the set. Structures are the objects in which first-order formulas are true or false. Groups, rings, ordered sets and graphs are all structures for suitable signatures.
Where this leads
27 pages build on this one.
- Ryll-Nardzewski theorem
- Ehrenfeucht–Fraïssé game
- Model theory
- O-minimal theory
- Elementary substructure
- Amalgamation property
- Dense linear order
- Second-order logic
- Löwenheim–Skolem theorem
- Tarski–Vaught test
- Boolean-valued model
- Elementary embedding
- Fagin's theorem
- Stable theory
- Model
- Infinitary logic
- Lindström's theorem
- Elementary equivalence
- Fraïssé limit
- Substructure
- Satisfiability
- Higher-order logic
- Logical consequence
- Beth definability theorem
- Ultraproduct
- Łoś–Vaught test
- Definable set
Further reading
About this page
| Tag | 983GZBQYT4 |
|---|---|
| URI | m2://983GZBQYT4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Ehrenfeucht–Fraïssé game
- Model theory
- O-minimal theory
- Elementary substructure
- Amalgamation property
- Second-order logic
- Löwenheim–Skolem theorem
- Tarski–Vaught test
- Boolean-valued model
- Elementary embedding
- Fagin's theorem
- Model
- Infinitary logic
- Lindström's theorem
- Elementary equivalence
- Fraïssé limit
- Substructure
- Satisfiability
- Higher-order logic
- Logical consequence
- Beth definability theorem
- Ultraproduct
- Definable set