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Proceedings of the American Mathematical Society

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

 

 

Diophantine correct models of arithmetic


Author: L. Lipshitz
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
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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 [Enhancements On Off] (What's this?)

  • [1] Harvey Friedman, Countable models of set theories, Cambridge Summer School in Mathematical Logic (Cambridge, 1971) Springer, Berlin, 1973, pp. 539–573. Lecture Notes in Math., Vol. 337. MR 0347599
  • [2] Ju. V. Matijasevič, The Diophantineness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279–282 (Russian). MR 0258744

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DOI: https://doi.org/10.1090/S0002-9939-1979-0512068-1
Article copyright: © Copyright 1979 American Mathematical Society