2014/05/09 by Michael Pfender, Pfender, Michael
Computer Science · #03E35 #Constraint Satisfaction and Optimization #FOS: Mathematics #General Mathematics (math.GM) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation
paper · pdf · doi:10.48550/arxiv.1405.3944
openalex publication_date 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.