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Recursive fibers of RST isols


Author: T. G. McLaughlin
Journal: Proc. Amer. Math. Soc. 117 (1993), 1141-1147
MSC: Primary 03D50; Secondary 03C65
DOI: https://doi.org/10.1090/S0002-9939-1993-1116268-9
MathSciNet review: 1116268
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Abstract: Motivated by a conjecture of Ellentuck concerning fibers $ f_ \wedge ^{ - 1}(C),f$ recursive and $ C$ an element of one of Barback's "tame models" (Tame models in the isols, Houston J. Math. 12 (1986), 163-175), we study such fibers in the more general context of Nerode semirings. The principal results are that (1) all existentially complete Nerode semirings meet all of their recursive fibers, and (2) not all Nerode semirings meet all of their recursive fibers.


References [Enhancements On Off] (What's this?)

  • [1] J. Barback, Tame models in the isols, Houston J. Math. 12 (1986), 163-175. MR 862034 (88d:03090a)
  • [2] J. Hirschfeld, Models of arithmetic and recursive functions, Israel J. Math. 20 (1975), 111-126. MR 0381969 (52:2858)
  • [3] J. Hirschfeld and W. Wheeler, Forcing, arithmetic, and division rings, Lecture Notes in Math., vol. 454, Springer, Berlin, 1975. MR 0389581 (52:10412)
  • [4] T. McLaughlin, Regressive sets and the theory of isols, Lecture Notes in Pure and Appl. Math., vol. 66, Marcel Dekker, New York, 1982. MR 659652 (83i:03073)
  • [5] -, Nerode semirings and Barback's 'tame models,' Houston J. Math. 12 (1986), 211-223. MR 862038 (88d:03090b)
  • [6] -, Some properties of $ \forall \exists $ models in the isols, Proc. Amer. Math. Soc. 97 (1986), 495-502. MR 840636 (88b:03067)
  • [7] -, Sub-arithmetical ultrapowers: a survey, Ann. Pure Appl. Logic 49 (1990), 143-191. MR 1077076 (92k:03035)
  • [8] -, Recursive ultrapowers, simple models, and cofinal extensions, Arch. Math. Logic 31 (1992). MR 1155039 (93c:03044)
  • [9] A. Nerode, Extensions to isols, Ann. of Math. (2) 73 (1961), 362-403. MR 0131363 (24:A1215)
  • [10] -, Diophantine correct nonstandard models in the isols, Ann. of Math. (2) 84 (1966), 421-432. MR 0202603 (34:2465)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1116268-9
Keywords: Nerode semiring, recursive ultrapower, existential completeness
Article copyright: © Copyright 1993 American Mathematical Society

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