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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.

Information

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

REFERENCES

[1]Benham, R. D., private communication, 2006.Google Scholar
[2]Chang, C. C. and Keisler, H. J., Model theory, third ed., Studies in Logic and the Foundations of Mathematics, vol. 73, North-Holland Publishing Co., Amsterdam, 1990.Google Scholar
[3]Gaifman, H., A note on models and submodels of arithmetic, Conference in mathematical logic - London '70 (Hodges, W., editor), Lecture Notes in Mathematics, vol. 255, Springer-Verlag, Berlin and New York, 1972, pp. 128–144.CrossRefGoogle Scholar
[4]Meyer, R. K. and Mortensen, C., Inconsistent models for relevant arithmetics, this Journal, vol. 49 (1984), pp. 917–929.Google Scholar
[5]Mortensen, C., Inconsistent nonstandard arithmetic, this Journal, vol. 52 (1987), pp. 512–518.Google Scholar
[6]Mortensen, C., Inconsistent number systems, Notre Dame Journal of Formal Logic, vol. 29 ( 1987), pp. 45–60.CrossRefGoogle Scholar
[7]Paris, J. B. and Dimitracopoulos, C., Truth definitions for Δ0 formulae, Logic and algorithmic (Zurich, 1980), Monographie Enseignement Mathématique, vol. 30, Univ. Geneve, Geneva, 1982, pp. 317–329.Google Scholar
[8]Paris, J. B. and Pathmanathan, N., A note on Priest's finite inconsistent arithmetics, Journal of Philosophical Logic, vol. 35 (2006), pp. 529–537.CrossRefGoogle Scholar
[9]Paris, J. B. and Pathmanathan, N., Erratum to ‘A note on Priest's finite inconsistent arithmetics’, (vol. 35 (2006), pp. 529–537), to appear in Journal of Philosophical Logic.CrossRefGoogle Scholar
[10]Priest, G., In contradiction, Nijhoff, Dordrecht, 1987.CrossRefGoogle Scholar
[11]Priest, G., Inconsistent models of arithmetic, Part I: Finite models, Journal of Philosophical Logic, vol. 26 (1997), pp. 223–235.CrossRefGoogle Scholar
[12]Priest, G., Inconsistent models of arithmetic, Part II: The general case, this Journal, vol. 65 (2000), pp. 1519–1529.Google Scholar