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Proceedings of the American Mathematical Society
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: 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.


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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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society