Mathematical logic and foundations Model theory: basic notions Concept
Model
Summary
A model of a theory is a structure in which every sentence of the theory is true. Models give meaning to axioms: the models of the group axioms are exactly the groups. A theory with a model is consistent, and by Gödel's completeness theorem every consistent first-order theory has a model.
Where this leads
21 pages build on this one.
- Strongly minimal theory
- Model theory
- Compactness theorem
- Skolem's paradox
- Omitting types theorem
- Saturated model
- Stable theory
- Model complete theory
- Prime model
- Lindström's theorem
- NIP theory
- Ax–Grothendieck theorem
- Complete theory
- Categorical theory
- Beth definability theorem
- Lefschetz principle
- Church's theorem on undecidability of first-order logic
- Type
- Tennenbaum's theorem
- Gödel's completeness theorem
- Vaught conjecture
Further reading
About this page
| Tag | MVCH6N9SNW |
|---|---|
| URI | m2://MVCH6N9SNW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07 |
| Changed | 2 November 2026 |
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Used by
- Strongly minimal theory
- Model theory
- Compactness theorem
- Skolem's paradox
- Omitting types theorem
- Saturated model
- Stable theory
- Model complete theory
- Prime model
- NIP theory
- Complete theory
- Categorical theory
- Beth definability theorem
- Type
- Tennenbaum's theorem
- Gödel's completeness theorem
- Vaught conjecture