On the minimality of tame models in the isols

Author:
Joseph Barback

Journal:
Proc. Amer. Math. Soc. **119** (1993), 935-939

MSC:
Primary 03D50; Secondary 11U09

MathSciNet review:
1155592

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Abstract: Based on the work of Hirschfeld, it is known that there is a close connection between models for the fragment of arithmetic and homomorphic images of the semiring of recursive functions. This fragment of arithmetic includes most of the familiar results of classical number theory. There is a realization of this fragment in the isols in systems called *tame models*. In this paper a new proof is given to the following result of Ellentuck and McLaughlin on the minimality of tame models: If two tame models share an infinite element, then the models are equal.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1155592-0

Article copyright:
© Copyright 1993
American Mathematical Society