Self-Inconsistency of set theory

 dc.contributor.author Pfender, Michael dc.date.accessioned 2021-12-17T10:14:55Z dc.date.available 2021-12-17T10:14:55Z dc.date.issued 2017-06-28 dc.description.abstract The consistency formula for set theory T e. g. Zermelo-Fraenkel set theory ZF, can be stated in form of a free-variable predicate in terms of the categorical theory PR of primitive recursive functions/maps/predicates. Free-variable p. r. predicates are decidable by T, key result. Decidability is built on recursive evaluation of p. r. map codes and soundness of that evaluation into theory T : internal, arithmetised p. r. map code equality is evaluated into map equality of T. In particular, thefree-variable p. r. consistency predicate of T is decidable by T. Therefore, by Gödel’s second incompleteness theorem, set theories T turn out to be self-inconsistent. en dc.identifier.issn 2197-8085 dc.identifier.uri https://depositonce.tu-berlin.de/handle/11303/15889 dc.identifier.uri http://dx.doi.org/10.14279/depositonce-14662 dc.language.iso en en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject.ddc 510 Mathematik en dc.subject.other free variables en dc.subject.other Skolem logic en dc.subject.other iteration en dc.subject.other primitive recursion en dc.subject.other gödelisation en dc.subject.other map code evaluation en dc.subject.other objectivity en dc.subject.other arithmetised equality en dc.subject.other soundness en dc.subject.other predicates en dc.subject.other decidability en dc.subject.other Gödel theorems en dc.subject.other inconsistency provability en dc.title Self-Inconsistency of set theory en dc.type Research Paper en dc.type.version submittedVersion en tub.accessrights.dnb free en tub.affiliation Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik de tub.affiliation.faculty Fak. 2 Mathematik und Naturwissenschaften de tub.affiliation.institute Inst. Mathematik de tub.publisher.universityorinstitution Technische Universität Berlin en tub.series.issuenumber 2017, 08 en tub.series.name Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin en tub.subject.msc2000 03B30 Foundations of classical theories en tub.subject.msc2000 18-02 Research exposition en

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