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On LP-models of arithmetic

Published online by Cambridge University Press:  12 March 2014

J. B. Paris  and
A. Sirokofskich
J. B. Paris
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom, E-mail: jeff.paris@manchester.ac.uk
A. Sirokofskich
Affiliation:
Department of Mathematics, University of Athens, GR-157 84 Zografou, Greece, E-mail: asirokofski@gmail.com
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Abstract

We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(ℕ) essentially arise via congruence relations on classical models of Th(ℕ). We also show that the analogue of Priest's Conjecture for IΔ0 + Exp implies the existence of truth definitions for intervals [0, a] ⊂eM ⊨ IΔ0 + Exp in any cut [0, a] ⊂eK ⊆eM closed under successor and multiplication.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 1 , March 2008 , pp. 212 - 226
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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