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arXiv · 1405.3944

Consistency Decision

Michael Pfender
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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, ω-consistency assumed. By Gödel's second incompleteness theorem on undecidability of set theory's consistency formula by set theory under assumption of this ω- consistency, classical set theory turns out to be ω-inconsistent.

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Michael Pfender. 2014-05-09. Consistency Decision. https://arxiv.org/abs/1405.3944

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