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Consistency Decision I: Self-Inconsistency

Pfender, Michael

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

The consistency formula for gödelian Arithmetics T can be stated as free-variable predicate in terms of the categorical theory PR of primitive recursive functions/maps/predicates. Free-variable p.r. predicates are decidable by gödelian theory T, key result, built on recursive evaluation of p.r. map codes and soundness of that evaluation into theories T : internal, arithmetised p. r. map code equality is evaluated into map equality of T. In particular the free-variable p.r. consistency predicate of T is decided by T. Therefore, by Gödel's second incompleteness theorem, gödelian quantified Arithmetics T turn out to be self-inconsistent.