Inconsistency of set theory via evaluation
| dc.contributor.author | Pfender, Michael | |
| dc.contributor.author | Nguyen, C.C. | |
| dc.contributor.author | Sablatnig, J. | |
| dc.date.accessioned | 2021-12-17T10:16:14Z | |
| dc.date.available | 2021-12-17T10:16:14Z | |
| dc.date.issued | 2020-07-28 | |
| dc.description.abstract | We 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.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15925 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14698 | |
| 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 | classical first-order logic | en |
| dc.subject.other | Goedel numberings | en |
| dc.subject.other | issues of incompleteness | en |
| dc.subject.other | foundations | en |
| dc.subject.other | deductive systems | en |
| dc.title | Inconsistency of set theory via evaluation | 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 | 2020, 04 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 03B10 Classical first-order logic | en |
| tub.subject.msc2000 | 03F40 Gödel numberings in proof theory | en |
| tub.subject.msc2000 | 18A15 Foundations, relations to logic and deductive systems | en |
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