Definition of Axiomatizable. Meaning of Axiomatizable. Synonyms of Axiomatizable

- model theory, a branch of mathematical logic, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first-order...
- mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification...
- theory that can be axiomatized without schemata is said to be finitely axiomatizable. All theorems of ZFC are also theorems of von Neumann–Bernays–Gödel...
- theory for which there is an independent set of axioms is independently axiomatizable. Some authors say that σ is independent of T when T simply cannot prove...
- axiomatizable, even when it is recursively axiomatizable. (Note that a logic is recursively enumerable if and only if it is recursively axiomatizable...
- omitting the multiplication operation entirely. The theory is com****bly axiomatizable; the axioms include a schema of induction. Presburger arithmetic is...
- \varphi } or T ⊢ ¬ φ {\displaystyle T\vdash \neg \varphi } ). Recursively axiomatizable first-order theories that are consistent and rich enough to allow general...
- coming up with a counterexample: Robinson arithmetic Q. Q is finitely axiomatizable because it lacks Peano arithmetic's axiom schema of induction; nevertheless...
- imaginaries; be finitely axiomatizable; be decidable: There is an algorithm to decide which statements are provable; be recursively axiomatizable; be model complete...
- well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem...