Measure and cupping in the Turing degrees

Authors:
George Barmpalias and Andrew E. M. Lewis

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3607-3622

MSC (2010):
Primary 03D28; Secondary 03D10

Published electronically:
February 6, 2012

MathSciNet review:
2929029

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Abstract | References | Similar Articles | Additional Information

Abstract: We answer a question of Jockusch by showing that the measure of the Turing degrees that satisfy the cupping property is 0. In fact, every 2-random degree has a strong minimal cover and so fails to satisfy the cupping property.

**[BDN11]**George Barmpalias, Rod Downey, and Keng-Meng Ng.

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Measure, category, and degrees of unsolvability.

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Additional Information

**George Barmpalias**

Affiliation:
Institute for Logic, Language and Computation, Universiteit van Amsterdam 1090 GE, P.O. Box 94242, The Netherlands

Email:
barmpalias@gmail.com

**Andrew E. M. Lewis**

Affiliation:
School of Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom

Email:
andy@aemlewis.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11183-9

Received by editor(s):
January 24, 2011

Received by editor(s) in revised form:
March 11, 2011, and April 5, 2011

Published electronically:
February 6, 2012

Additional Notes:
The second author was supported by a Royal Society University Research Fellowship.

Communicated by:
Julia Knight

Article copyright:
© Copyright 2012
American Mathematical Society