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Proceedings of the American Mathematical Society

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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 $ \Pi _2^0$ 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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Article copyright: © Copyright 1993 American Mathematical Society

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