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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Diophantine correct models of arithmetic
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by L. Lipshitz PDF
Proc. Amer. Math. Soc. 73 (1979), 107-108 Request permission

Abstract:

A countable nonstandard model of arithmetic is diophantine correct if and only if it can be embedded in arbitrarily short nonstandard initial segments of itself.
References
  • Harvey Friedman, Countable models of set theories, Cambridge Summer School in Mathematical Logic (Cambridge, 1971) Lecture Notes in Math., Vol. 337, Springer, Berlin, 1973, pp. 539–573. MR 0347599
  • Ju. V. Matijasevič, The Diophantineness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279–282 (Russian). MR 0258744
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 73 (1979), 107-108
  • MSC: Primary 03H15; Secondary 03C62, 10N15
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0512068-1
  • MathSciNet review: 512068