Noninfinitary
Noninfinitary refers to systems, languages, or methods in logic and mathematics that do not employ infinitary operations. In this context, all expressions, proofs, and syntactic constructions are finite in length. The term is used to contrast finitary or standard approaches with infinitary logics, which permit infinite conjunctions, disjunctions, or quantifier structures.
In logic, the prototypical noninfinitary framework is first-order logic (FOL), along with propositional logic. FOL formulas
The choice of noninfinitary systems supports important meta-theoretic properties. For example, first-order logic enjoys the completeness
Applications of noninfinitary formalisms span mathematics, computer science, and formal reasoning. They underpin everyday formalizations, programming
See also: infinitary logic, first-order logic, finite model theory, proof theory.