Consistency Decision

Abstract

The consistency formula for set theory can be stated in terms of the free-variables theory of primitive recursive maps. Free-variable p. r. predicates are decidable by set theory, main result here, built on recursive evaluation of p. r. map codes and soundness of that evaluation in set theoretical frame: internal p. r. map code equality is evaluated into set theoretical equality. So the free-variable consistency predicate of set theory is decided by set theory, {\omega}-consistency assumed. By G\"odel's second incompleteness theorem on undecidability of set theory's consistency formula by set theory under assumption of this {\omega}- consistency, classical set theory turns out to be {\omega}-inconsistent.