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On the structure of nonstandard models of arithmetic


Author: R. G. Phillips
Journal: Proc. Amer. Math. Soc. 27 (1971), 359-363
MSC: Primary 02.57
DOI: https://doi.org/10.1090/S0002-9939-1971-0274268-0
MathSciNet review: 0274268
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Abstract: In this paper we show that the additive group of each nonstandard model $ ^ \ast Z$ of the integers $ Z$ is isomorphic to the group $ \left\langle {F \times Z, + } \right\rangle $ where $ F$ is a direct sum of $ \alpha $-copies of the rational $ Q,\alpha $ the cardinality of $ ^ \ast Z$, and + is defined by: $ (a,x) + (b,y) = (a + b,x + y + g(a,b))$ for certain functions $ g$ mapping from $ F \times F$ to $ Z$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0274268-0
Keywords: Nonstandard models, additive groups, nonstandard models of arithmetic, Goldbach's conjecture
Article copyright: © Copyright 1971 American Mathematical Society

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