Consistency Decision I: Self-Inconsistency

dc.contributor.authorPfender, Michael
dc.date.accessioned2021-12-17T10:14:19Z
dc.date.available2021-12-17T10:14:19Z
dc.date.issued2016-07-22
dc.description.abstractThe 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.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15872
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14645
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherprimitive recursionen
dc.subject.othercategorical free-variables Arithmeticen
dc.subject.othercode evaluationen
dc.subject.othersoundnessen
dc.subject.otherdecidability of PR predicatesen
dc.subject.otherGoedel theoremsen
dc.subject.otherself-inconsistency of quantified arithmetical theoriesen
dc.titleConsistency Decision I: Self-Inconsistencyen
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.issuenumber2016, 14en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200003F03 Proof theory, generalen
tub.subject.msc200018A05 Definitions, generalizationsen
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