First-Order Theory
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
A set of sentences expressed in first-order logic over a fixed signature, closed under logical consequence, that specifies properties intended to hold in structures of that signature.
First-Order Theory
- Pure Mathematics -
Algebra Dictionary
Definition
A set of first‑order sentences in a fixed signature (vocabulary) — closed or considered as a generating set for its deductive closure — whose intended models are the structures that satisfy every sentence in the set.