Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14698
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Main Title: Inconsistency of set theory via evaluation
Author(s): Pfender, Michael
Nguyen, C.C.
Sablatnig, J.
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15925
http://dx.doi.org/10.14279/depositonce-14698
License: http://rightsstatements.org/vocab/InC/1.0/
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.
Subject(s): classical first-order logic
Goedel numberings
issues of incompleteness
foundations
deductive systems
Issue Date: 28-Jul-2020
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 03B10 Classical first-order logic
03F40 Gödel numberings in proof theory
18A15 Foundations, relations to logic and deductive systems
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2020, 04
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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