Some properties of models in the isols
Author:
T. G. McLaughlin
Journal:
Proc. Amer. Math. Soc. 97 (1986), 495502
MSC:
Primary 03D50; Secondary 03C62, 03H15
MathSciNet review:
840636
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Abstract: It is a consequence of theorems proved by Nerode [10] and Hirschfeld [7] that every countable model of arithmetic is isomorphic to a subsemiring of a onegenerator semiring of isols. We characterize, in terms of the generators of "Nerode semirings", the contents of arbitrary semirings of isols that are models of arithmetic, and we show that all such are in fact models of the true sentences of isol theory. We solve one of the chief problems left open in [8], and in we provide an example of the applied virtues of correct subsemirings of the isols.
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 J. Barback, Tame models in the isols, Houston J. Math. (to appear). MR 862034 (88d:03090a)
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 J. C. E. Dekker and J. Myhill, The divisibility of isols by powers of primes, Math. Z. 73 (1960), 127133. MR 0112840 (22:3689)
 [3]
 , Recursive equivalence types, Univ. Calif. Publ. Math. (N.S.) 3 (1960), 67214. MR 0117155 (22:7938)
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 E. Ellentuck, A coding theorem for isols, J. Symbolic Logic 35 (1970), 378382. MR 0282833 (44:67)
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 , Diagonal methods in the theory of isols, Z. Math. Logik Grundlag. Math. 26 (1980), 193204. MR 578828 (81i:03071)
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 J. Hirschfeld, Models of arithmetic and recursive functions, Israel J. Math. 20 (1975), 111126. MR 0381969 (52:2858)
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 A. Nerode, Diophantine correct nonstandard models in the isols, Ann. of Math. 84 (1966), 421432. MR 0202603 (34:2465)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919860840636X
PII:
S 00029939(1986)0840636X
Keywords:
Isol,
Model of arithmetic,
Nerode semiring
Article copyright:
© Copyright 1986
American Mathematical Society
