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Proceedings of the American Mathematical Society

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



Enumerations, countable structures
and Turing degrees

Author: Stephan Wehner
Journal: Proc. Amer. Math. Soc. 126 (1998), 2131-2139
MSC (1991): Primary 03D45
MathSciNet review: 1443415
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proven that there is a family of sets of natural numbers which has enumerations in every Turing degree except for the recursive degree. This implies that there is a countable structure which has representations in all but the recursive degree. Moreover, it is shown that there is such a structure which has a recursively represented elementary extension.

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

  • 1. Christopher J. Ash, Carl G. Jockusch, jr. and Julia F. Knight; Jumps of orderings, Trans. Amer. Math. Soc., vol. 319, (1990), p. 573 - 599. MR 90j:03081
  • 2. Julia F. Knight; Degrees Coded in Jumps of Orderings, J. Symbolic Logic, vol. 51, (1986), p. 1034 - 1042. MR 88j:03030
  • 3. Linda J. Richter; Degrees of Structures, J. Symbolic Logic, vol. 46 (1981), p. 723 - 731. MR 83d:03048
  • 4. Theodore A. Slaman; Relative to any Nonrecursive Set, Proc. Amer. Math. Soc., vol. 126 (1998), 2117-2122. CMP 97:11
  • 5. Robert I. Soare; Recursively Enumerable Sets and Degrees, Springer Verlag, Berlin, Heidelberg, New York, Tokyo, 1987. MR 88m:03003
  • 6. Stephan Wehner; On Injective Enumerability of Recursively Enumerable Classes of Cofinite Sets, Arch. Math. Logic, vol. 34, (1995), p. 183 - 196. MR 96d:03062
  • 7. C.E.M. Yates; On the Degrees of Index Sets II, Trans. Amer. Math.Soc., vol. 135 (1969), p. 249 - 266. MR 39:2637

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Additional Information

Stephan Wehner
Affiliation: Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

Received by editor(s): September 17, 1996
Received by editor(s) in revised form: January 6, 1997
Additional Notes: Many thanks go to Julia Knight and Carl Jockusch!
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1998 American Mathematical Society