Mathematical logic and foundations Model theory: basic notions Concept
Complete theory
Summary
A complete theory is a satisfiable theory that decides every sentence of its language: it implies the sentence or its negation. All models of a complete theory are elementarily equivalent. The theory of a single structure is always complete, and proving that a list of axioms is complete is a central task of model theory.
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About this page
| Tag | 655K8Y7VS8 |
|---|---|
| URI | m2://655K8Y7VS8 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C35, 03C07 |
| Specializes | Theory |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Ryll-Nardzewski theorem
- Strongly minimal theory
- Presburger arithmetic
- Stable theory
- Real closed field
- Prime model
- NIP theory
- Morley's categoricity theorem
- Gödel's incompleteness theorems
- Vaught conjecture
- Łoś–Vaught test