The second incompleteness theorem and bounded interpretations
type: Item
instance of: scholarly article
title: The second incompleteness theorem and bounded interpretations
zbMATH Open document ID: 1260.03109
author: Albert Visser
published in: Studia Logica
publication date: 2012-10-01T00:00:00Z
review text: Let \(\mathrm{con}_i(U)\) be consistency of a theory \(U\) for provability involving axioms witnessed below \(i\). Let \(\mathrm{slb-con}(U)\) (super-logarithmically bounded consistency of \(U\)) mean \(\forall x( \mathrm{superexp}(x)\downarrow\iff \mathrm{con}_x(U))\). It is proved that \(C=\mathrm{slb-con}(S^1_2)\) is an Orey sentence for Kalmar-elementary arithmetic EA, i.e., EA interprets both \(\mathrm{EA}+\mathrm C\) and \(\mathrm{EA}+\neg \mathrm C\). Therefore C is independent of EA although it is weaker than \(\mathrm{con}(\mathrm{EA})\).
Mathematics Subject Classification ID: 03F25
Mathematics Subject Classification ID: 03F40
zbMATH DE Number: 6088848
zbMATH Keywords: second incompleteness theorem
zbMATH Keywords: interpretability
reviewed by: G. E. Mints
MaRDI profile type: Publication
full work available at URL: s11225-012-9385-z
OpenAlex ID: W1980167452
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DOI: 10.1007/S11225-012-9385-Z
description: scientific article; zbMATH DE number 6088848