Preservation theorems and restricted consistency statements in bounded arithmetic
type: Item
instance of: scholarly article
title: Preservation theorems and restricted consistency statements in bounded arithmetic
zbMATH Open document ID: 1060.03080
author: Arnold Beckmann
published in: Annals of Pure and Applied Logic
publication date: 2004-08-06T00:00:00Z
review text: In the paper a new restricted consistency notion RCON\(^{\ast}(T^{j}_{2})\) for bounded arithmetic theories \(T^{j}_{2}\) is introduced and studied. It is the strongest \(\forall \Pi^{b}_{1}\)-statement over \(S^{1}_{2}\) provable in \(T^{j}_{2}\), similar to \(\text{Con}(G_{i})\) of Krajiček and Pudlák or \(\text{RCON}(T{i}_{1})\) of Krajiček and Takeuti. The advantage of the introduced new notion is that it can directly be used to construct models of \(T^{j}_{2}\). It is applied by proving preservation theorems for certain theories of bounded arithmetic.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03F25
zbMATH DE Number: 2083182
zbMATH Keywords: Bounded arithmetic
zbMATH Keywords: Restricted consistency
zbMATH Keywords: Preservation theorems
MaRDI profile type: Publication
full work available at URL: j.apal.2003.11.003
OpenAlex ID: W2005184534
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DOI: 10.1016/J.APAL.2003.11.003
description: scientific article; zbMATH DE number 2083182