  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.
