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Enumerations, countable structures and Turing degrees
Author(s):
Stephan
Wehner
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2131-2139.
MSC (1991):
Primary 03D45
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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:
- 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
Email:
stephan@pepe.chem.ubc.ca
DOI:
10.1090/S0002-9939-98-04314-7
PII:
S 0002-9939(98)04314-7
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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