Self-Inconsistency of set theory

dc.contributor.authorPfender, Michael
dc.date.accessioned2021-12-17T10:14:55Z
dc.date.available2021-12-17T10:14:55Z
dc.date.issued2017-06-28
dc.description.abstractThe 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.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15889
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14662
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherfree variablesen
dc.subject.otherSkolem logicen
dc.subject.otheriterationen
dc.subject.otherprimitive recursionen
dc.subject.othergödelisationen
dc.subject.othermap code evaluationen
dc.subject.otherobjectivityen
dc.subject.otherarithmetised equalityen
dc.subject.othersoundnessen
dc.subject.otherpredicatesen
dc.subject.otherdecidabilityen
dc.subject.otherGödel theoremsen
dc.subject.otherinconsistency provabilityen
dc.titleSelf-Inconsistency of set theoryen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2017, 08en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200003B30 Foundations of classical theoriesen
tub.subject.msc200018-02 Research expositionen

Files

Original bundle
Now showing 1 - 1 of 1
Loading…
Thumbnail Image
Name:
Preprint-08-2017.pdf
Size:
382.43 KB
Format:
Adobe Portable Document Format

Collections