Proceedings of the American Mathematical Society

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



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: 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.

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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

Andrew E. M. Lewis
Affiliation: School of Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom

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