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

 

Global properties of the lattice of $\Pi^0_1$ classes


Authors: Douglas Cenzer and André Nies
Journal: Proc. Amer. Math. Soc. 132 (2004), 239-249
MSC (2000): Primary 03D25
Published electronically: May 7, 2003
MathSciNet review: 2021268
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Abstract: Let $\mathcal{E}_\Pi$ be the lattice of $\Pi^0_1$ classes of reals. We show there are exactly two possible isomorphism types of end intervals, $[P,2^\omega]$. Moreover, finiteness is first order definable in $\mathcal{E}_\Pi$.


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Additional Information

Douglas Cenzer
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: cenzer@math.ufl.edu

André Nies
Affiliation: Department of Mathematics, The University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637
Address at time of publication: Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1020, New Zealand
Email: nies@math.uchicago.edu, andre@cs.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06984-3
PII: S 0002-9939(03)06984-3
Keywords: $\Pi^0_1$ classes, definability, end segments
Received by editor(s): June 4, 2002
Received by editor(s) in revised form: August 19, 2002
Published electronically: May 7, 2003
Additional Notes: The second author was partially supported by NSF grant DMS–9803482
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2003 American Mathematical Society