Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14662
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Main Title: Self-Inconsistency of set theory
Author(s): Pfender, Michael
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15889
http://dx.doi.org/10.14279/depositonce-14662
License: http://rightsstatements.org/vocab/InC/1.0/
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.
Subject(s): free variables
Skolem logic
iteration
primitive recursion
gödelisation
map code evaluation
objectivity
arithmetised equality
soundness
predicates
decidability
Gödel theorems
inconsistency provability
Issue Date: 28-Jun-2017
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 03B30 Foundations of classical theories
18-02 Research exposition
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2017, 08
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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