Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1155592-0
Article copyright: © Copyright 1993 American Mathematical Society