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Proceedings of the American Mathematical Society

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Relative to any nonrecursive set


Author: Theodore A. Slaman
Journal: Proc. Amer. Math. Soc. 126 (1998), 2117-2122
MSC (1991): Primary 03C57, 04D45
DOI: https://doi.org/10.1090/S0002-9939-98-04307-X
MathSciNet review: 1443408
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Abstract: There is a countable first order structure $\mathfrak{M}$ such that for any set of integers $X$, $X$ is not recursive if and only if there is a presentation of $\mathfrak{M}$ which is recursive in $X$.


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

  • [Kleene and Post] Kleene, S. C. and Post, E. L. [1954]. The upper semi-lattice of degrees of recursive unsolvability, Anal. Math. 59: 379-407. MR 15:772a
  • [Wehner] Wehner, S. [1996]. Enumerations, countable structures and Turing degrees, Proc. Amer. Math. Soc. 126 (1998), 2131-2139. CMP 97:11

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Additional Information

Theodore A. Slaman
Email: ted@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04307-X
Keywords: Recursive model theory
Received by editor(s): May 10, 1996
Received by editor(s) in revised form: December 17, 1996
Additional Notes: During the preparation of this paper, Slaman was partially supported by National Science Foundation Grant DMS-9500878.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1998 American Mathematical Society