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Inconsistent models of arithmetic Part II: the general case

  • Graham Priest (a1)
Abstract
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.

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[1]Bell J. L. and Slomson A., Models and Ultraproducts: an Introduction, North Holland, Amsterdam, 1969.
[2]Kaye R., Models ofPeano Arithmetic, Clarendon Press, Oxford, 1991.
[3]Mortensen C., Inconsistent Mathematics, Kluwer Academic Publishers, Dordrecht, 1995.
[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.
[5]Priest G., In Contradiction, Martinus Nijhoff, the Hague, 1987.
[6]Priest G., Is Arithmetic Consistent?, Mind, vol. 103 (1994), pp. 337–49.
[7]Priest G., Inconsistent Models of Arithmetic, Part I: Finite Models, Journal of Philosophical Logic, vol. 26 (1997), pp. 223–35.
[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. 6179.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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