Mathematical logic and foundations Model theory: basic notions Concept
Theory
Summary
A theory in a first-order language is a set of sentences of that language. Its sentences play the role of axioms, such as the axioms of groups or of fields. Theories are the syntactic side of model theory, and the structures in which all their sentences hold are their models.
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| Tag | 92SWXST1ZM |
|---|---|
| URI | m2://92SWXST1ZM |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07, 03B10 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Model theory
- O-minimal theory
- Löb's theorem
- Diagonal lemma
- Omitting types theorem
- Model
- Model complete theory
- Complete theory
- Categorical theory
- Quantifier elimination
- Beth definability theorem
- Robinson arithmetic
- Type
- Gödel's incompleteness theorems
- Second-order arithmetic