The additive structure of models of arithmetic

Lipshitz, Leonard; Nadel, Mark

doi:10.1090/S0002-9939-1978-0491158-5

The additive structure of models of arithmetic
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by Leonard Lipshitz and Mark Nadel PDF

Proc. Amer. Math. Soc. 68 (1978), 331-336 Request permission

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

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Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt

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