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The additive structure of models of arithmetic


Authors: Leonard Lipshitz and Mark Nadel
Journal: Proc. Amer. Math. Soc. 68 (1978), 331-336
MSC: Primary 02H20
DOI: https://doi.org/10.1090/S0002-9939-1978-0491158-5
MathSciNet review: 0491158
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Abstract: It is shown that for a model of Presburger arithmetic to have an expansion to a model of Peano arithmetic it is necessary that the model be recursively saturated. For countable models this condition is also sufficient; for uncountable models it is not.


References [Enhancements On Off] (What's this?)

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  • [2] K. J. Barwise and John Schlipf, An introduction to recursively saturated and resplendent models, J. Symbolic Logic 41 (1976), 531-536. MR 0403952 (53:7761)
  • [3] -, On recursively saturated models of arithmetic, Lecture Notes in Math., no. 498, Springer-Verlag, Berlin, 1975. MR 0409172 (53:12934)
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  • [6] H. J. Keisler, Model theory for infinitary logic, North-Holland, Amsterdam, 1971. MR 0344115 (49:8855)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0491158-5
Article copyright: © Copyright 1978 American Mathematical Society

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