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Inconsistent models of arithmetic Part II: the general case

Published online by Cambridge University Press:  12 March 2014

Graham Priest
Graham Priest*
Affiliation:
Department of Philosophy, University of Queensland, Brisbane, Australia, 4072, E-mail:[email protected]
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Abstract

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal, of the rationals, or of any other order type that can be embedded in the rationals in a certain way.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1519 - 1529
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Bell, J. L. and Slomson, A., Models and Ultraproducts: an Introduction, North Holland, Amsterdam, 1969.Google Scholar
[2]Kaye, R., Models ofPeano Arithmetic, Clarendon Press, Oxford, 1991.CrossRefGoogle Scholar
[3]Mortensen, C., Inconsistent Mathematics, Kluwer Academic Publishers, Dordrecht, 1995.CrossRefGoogle Scholar
[4]Priest, G., On Alternative Geometries, Arithmetics and Logics; a Tribute to Łukasiewicz, Proceedings of the Conference Łukasiewicz in Dublin, 1996 (M. Baghramian, editor), to appear.Google Scholar
[5]Priest, G., In Contradiction, Martinus Nijhoff, the Hague, 1987.CrossRefGoogle Scholar
[6]Priest, G., Is Arithmetic Consistent?, Mind, vol. 103 (1994), pp. 337–49.CrossRefGoogle Scholar
[7]Priest, G., Inconsistent Models of Arithmetic, Part I: Finite Models, Journal of Philosophical Logic, vol. 26 (1997), pp. 223–35.CrossRefGoogle Scholar
[8]van Bendegem, J.-P., Strict, Yet Rich Finitism, First International Symposium on GÖdel's Theorems (Wolkowski, W., editor), World Scientific Press, Singapore, 1993, pp. 61–79.Google Scholar