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.
Where this leads
19 pages build on this one.
- Model theory
- O-minimal theory
- Löb's theorem
- Diagonal lemma
- Elementary class
- Omitting types theorem
- Łoś–Tarski preservation theorem
- Model
- Model complete theory
- Tarski's axioms
- Complete theory
- Gentzen's consistency proof
- Categorical theory
- Quantifier elimination
- Beth definability theorem
- Robinson arithmetic
- Type
- Gödel's incompleteness theorems
- Second-order arithmetic
Further reading
About this page
| Tag | 92SWXST1ZM |
|---|---|
| URI | m2://92SWXST1ZM |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07, 03B10 |
| Same as |
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Used by
- Model theory
- O-minimal theory
- Löb's theorem
- Diagonal lemma
- Elementary class
- Omitting types theorem
- Łoś–Tarski preservation theorem
- Model
- Model complete theory
- Tarski's axioms
- Complete theory
- Categorical theory
- Quantifier elimination
- Beth definability theorem
- Robinson arithmetic
- Type
- Gödel's incompleteness theorems
- Second-order arithmetic