Slow consistency
type: Item
instance of: scholarly article
title: Slow consistency
zbMATH Open document ID: 1263.03055
author: Michael Rathjen
author: Andreas Weiermann
author: Sy-David Friedman
published in: Annals of Pure and Applied Logic
publication date: 2013-02-19T00:00:00Z
review text: The authors introduce the notion of slow consistency \(\mathrm{Con}^*(\mathrm{PA})\) of Peano arithmetic \(\mathrm{PA}\): ``For all \(x\), the theory consisting of the first \(f(x)\) non-logical axioms of \(\mathrm{PA}\) is consistent'', where \(f\) is a certain slow-growing computable function. Then the authors prove that the strength of the theory \(\mathrm{PA} + \mathrm{Con}^*(\mathrm{PA})\) is strictly between the strength of the theory \(\mathrm{PA}\) and the strength of the theory \(\mathrm{PA} + \mathrm{Con}(\mathrm{PA})\).
reviewed by: Jaime Gaspar
Mathematics Subject Classification ID: 03F25
Mathematics Subject Classification ID: 03F05
Mathematics Subject Classification ID: 03F15
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 6137405
zbMATH Keywords: Peano arithmetic
zbMATH Keywords: consistency strength
zbMATH Keywords: interpretation
zbMATH Keywords: fast-growing function
zbMATH Keywords: slow consistency
zbMATH Keywords: Orey sentence
Wikidata QID: Q60500825
MaRDI profile type: Publication
full work available at URL: j.apal.2012.11.009
OpenAlex ID: W4206512100
DOI: 10.1016/J.APAL.2012.11.009
DBLP publication ID: journals/apal/FriedmanRW13
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description: scientific article; zbMATH DE number 6137405