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Main Title: Arithmetical Foundations: Recursion. Evaluation. Consistency
Author(s): Pfender, Michael
Type: Research Paper
Abstract: Gödel Theorems revisited. Categorical free-variables theory of Primitive Recursion and of mu-recursion. Definition of evaluation of PR codes as Complexity Controlled Iteration, introduction of a theory piR of non-infinite descent of such iterations. (Termination conditioned) Soundness of evaluation. Decidability of PR free-variable predicates. Decidability of Consistency formulae for piR and set theory as special cases. omega-inconsistency of set theory and derivability of consistency formula for Descent theory piR as consequences.
Subject(s): Gödel Theorems
categorical recursion
consistency provability
Issue Date: 21-Dec-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 03G30 Categorical logic, topoi
03B30 Foundations of classical theories
03D75 Abstract and axiomatic computability and recursion theory
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 38
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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