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Contiguity and distributivity in the enumerable Turing degrees

Published online by Cambridge University Press:  12 March 2014

Rodney G. Downey  and
Steffen Lempp
Rodney G. Downey
Affiliation:
Department of Mathematics, Victoria University, P. O. Box 600 Wellington, New Zealand E-mail: Rod.Downey@VUW.AC.NZ
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison WI 53706, USA E-mail: Lempp@math.wisc.edu
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Abstract

We prove that a (recursively) enumerable degree is contiguous iff it is locally distributive. This settles a twenty-year old question going back to Ladner and Sasso. We also prove that strong contiguity and contiguity coincide, settling a question of the first author, and prove that no m-topped degree is contiguous, settling a question of the first author and Carl Jockusch [11]. Finally, we prove some results concerning local distributivity and relativized weak truth table reducibility.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1215 - 1240
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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