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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

The finite intervals of the Muchnik lattice


Author: Sebastiaan A. Terwijn
Journal: Trans. Amer. Math. Soc. 364 (2012), 2521-2538
MSC (2010): Primary 03D30, 03G10, 06B05, 06D20
Published electronically: December 16, 2011
MathSciNet review: 2888218
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Abstract: We characterize the finite intervals of the Muchnik lattice by proving that they form a certain proper subclass of the finite distributive lattices. We also discuss infinite intervals, mainly to conclude that much more is possible here than for the related Medvedev lattice.


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Additional Information

Sebastiaan A. Terwijn
Affiliation: Department of Mathematics, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, the Netherlands
Email: terwijn@math.ru.nl

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05384-5
Keywords: Muchnik lattice, finite distributive lattices, Turing degrees
Received by editor(s): April 6, 2009
Received by editor(s) in revised form: May 24, 2010
Published electronically: December 16, 2011
Additional Notes: This research was supported by the Austrian Science Fund FWF under project P18713-N18.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.