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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A minimal pair of $K$-degrees


Authors: Barbara F. Csima and Antonio Montalbán
Journal: Proc. Amer. Math. Soc. 134 (2006), 1499-1502
MSC (2000): Primary 03D30
Published electronically: October 4, 2005
MathSciNet review: 2199198
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Abstract: We construct a minimal pair of $K$-degrees. We do this by showing the existence of an unbounded nondecreasing function $f$ which forces $K$-triviality in the sense that $\gamma\in 2^\omega$ is $K$-trivial if and only if for all $n$, $K(\gamma\upharpoonright n) \leq K(n) + f(n)+ \mathcal{O}(1)$.


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Additional Information

Barbara F. Csima
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Address at time of publication: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: csima@math.cornell.edu; csima@math.uwaterloo.ca

Antonio Montalbán
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Address at time of publication: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: antonio@math.cornell.edu; antonio@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08086-X
PII: S 0002-9939(05)08086-X
Keywords: Minimal pair, relative randomness
Received by editor(s): November 19, 2004
Published electronically: October 4, 2005
Additional Notes: We thank Denis R. Hirschfeldt for bringing this question to our attention. The second author was partially supported by NSF Grant DMS-0100035.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.