Pfender, Michael2021-12-172021-12-172016-07-222197-8085https://depositonce.tu-berlin.de/handle/11303/15872http://dx.doi.org/10.14279/depositonce-14645The 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.en510 Mathematikprimitive recursioncategorical free-variables Arithmeticcode evaluationsoundnessdecidability of PR predicatesGoedel theoremsself-inconsistency of quantified arithmetical theoriesResearch Paper