The additive structure of models of arithmetic
- 1 January 1978
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 68 (3), 331-336
- https://doi.org/10.1090/s0002-9939-1978-0491158-5
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.Keywords
This publication has 4 references indexed in Scilit:
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- On recursively saturated models of arithmeticPublished by Springer Science and Business Media LLC ,1975
- Admissible Sets and StructuresPerspectives in Mathematical Logic, 1975
- The first order properties of products of algebraic systemsFundamenta Mathematicae, 1959