Inconsistency of set theory via evaluation

dc.contributor.authorPfender, Michael
dc.contributor.authorNguyen, C.C.
dc.contributor.authorSablatnig, J.
dc.date.accessioned2021-12-17T10:16:14Z
dc.date.available2021-12-17T10:16:14Z
dc.date.issued2020-07-28
dc.description.abstractWe introduce in an axiomatic way the categorical theory PR of primitive recursion as the initial cartesian category with Natural Numbers Object. This theory has an extension into constructive set theory S of primitive recursion with abstraction of predicates into subsets and two-valued (boolean) truth algebra. Within the framework of (typical) classical, quantified set theory T we construct an evaluation of arithmetised theory PR via Complexity Controlled Iteration with witnessed termination of the iteration, witnessed termination by availability of Hilbert s iota operator in set theory. Objectivity of that evaluation yields inconsistency of set theory T by a liar (anti)diagonal argument.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15925
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14698
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherclassical first-order logicen
dc.subject.otherGoedel numberingsen
dc.subject.otherissues of incompletenessen
dc.subject.otherfoundationsen
dc.subject.otherdeductive systemsen
dc.titleInconsistency of set theory via evaluationen
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.issuenumber2020, 04en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200003B10 Classical first-order logicen
tub.subject.msc200003F40 Gödel numberings in proof theoryen
tub.subject.msc200018A15 Foundations, relations to logic and deductive systemsen
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