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The strength of sharply bounded induction

✍ Scribed by Emil Jeřábek

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
186 KB
Volume
52
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We prove that the sharply bounded arithmetic T^0^~2~ in a language containing the function symbol ⌊x /2^y^ ⌋ (often denoted by MSP) is equivalent to PV~1~. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A Model-Theoretic Property of Sharply Bo
A Model-Theoretic Property of Sharply Bounded Formulae, with some Applications
✍ Jan Johannsen 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 581 KB

We define a property of substructures of models of arithmetic, that of being length-initial, and show that sharply bounded formulae are absolute between a model and its length-initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing a