Recursive fibers of RST isols
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- by T. G. McLaughlin PDF
- Proc. Amer. Math. Soc. 117 (1993), 1141-1147 Request permission
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
- Joseph Barback, Tame models in the isols, Houston J. Math. 12 (1986), no. 2, 163–175. MR 862034
- J. Hirschfeld, Models of arithmetic and recursive functions, Israel J. Math. 20 (1975), no. 2, 111–126. MR 381969, DOI 10.1007/BF02757881
- Joram Hirschfeld and William H. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Mathematics, Vol. 454, Springer-Verlag, Berlin-New York, 1975. MR 0389581
- Thomas G. McLaughlin, Regressive sets and the theory of isols, Lecture Notes in Pure and Applied Mathematics, vol. 66, Marcel Dekker, Inc., New York, 1982. MR 659652
- Joseph Barback, Tame models in the isols, Houston J. Math. 12 (1986), no. 2, 163–175. MR 862034
- T. G. McLaughlin, Some properties of $\forall \exists$ models in the isols, Proc. Amer. Math. Soc. 97 (1986), no. 3, 495–502. MR 840636, DOI 10.1090/S0002-9939-1986-0840636-X
- Thomas G. McLaughlin, Sub-arithmetical ultrapowers: a survey, Ann. Pure Appl. Logic 49 (1990), no. 2, 143–191. MR 1077076, DOI 10.1016/0168-0072(90)90064-9
- T. G. McLaughlin, Recursive ultrapowers, simple models, and cofinal extensions, Arch. Math. Logic 31 (1992), no. 4, 287–296. MR 1155039, DOI 10.1007/BF01794985
- Anil Nerode, Extensions to isols, Ann. of Math. (2) 73 (1961), 362–403. MR 131363, DOI 10.2307/1970338
- Anil Nerode, Diophantine correct non-standard models in the isols, Ann. of Math. (2) 84 (1966), 421–432. MR 202603, DOI 10.2307/1970455
Additional Information
- © Copyright 1993 American Mathematical Society
- 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