Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14673
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Main Title: On Hilbert's tenth problem: Is classical set theory inconsistent?
Author(s): Pfender, Michael
Sablatnig, Jan
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15900
http://dx.doi.org/10.14279/depositonce-14673
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We consider cartesian categorical (free-variables) theory PR of primitive recursion and arithmetise (gödelise) it into the natural numbers set of a classical set theory T: We evaluate the map codes of the coded theory by a general recursive T map and construct a μ-recursive decision algorithm based on evaluation of primitive recursive map codes. Within theory T strengthend by p. r. internal inconsistency axiom, the predicate decision algorithm turns out to be total, terminating. It decides in a uniform way all diophantine equations and contradicts within the strengthend theory Matiyasevich's negative solution of Hilbert's 10th problem. But by Gödel's second incompleteness theorem the strengthend theory is relative consistent to T: This is to show inconsistency of classical set theorie(s).
Subject(s): recursive functions
recursive relations
subrecursive hierarchies
Hilbert’s tenth problem
classical set theory
Issue Date: 12-Oct-2018
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 03D20 Recursive functions and relations, subrecursive hierarchies
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2018, 11
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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