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Main Title: Consistency Decision I: Self-Inconsistency
Author(s): Pfender, Michael
Type: Research Paper
Abstract: The 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.
Subject(s): primitive recursion
categorical free-variables Arithmetic
code evaluation
decidability of PR predicates
Goedel theorems
self-inconsistency of quantified arithmetical theories
Issue Date: 22-Jul-2016
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 03F03 Proof theory, general
18A05 Definitions, generalizations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2016, 14
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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