A first-order sentence is provable from a theory T if and only if it holds in every model of T (T ⊨ φ ⇔ T ⊢ φ). First-order logic is complete with respect to its standard semantics — distinct from the incompleteness theorems, which target…
Gödel's completeness theorem
Related concepts
- Universal quantifier
- Existential quantifier
- Tarski semantic definition of truth
- Craig interpolation theorem
- Herbrand's theorem
- Cut-elimination (Gentzen Hauptsatz)
- Compactness theorem (Godel-Malcev)
- Kleene recursion theorem
- Rice theorem (1953)
- Arithmetic hierarchy (Sigma_n / Pi_n)
- Priority method (Friedberg-Muchnik 1956)
- Equational completeness (Birkhoff 1935)
- Quasivariety (Mal cev / McKenzie)