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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Global properties of the lattice of $\Pi ^0_1$ classes
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by Douglas Cenzer and André Nies PDF
Proc. Amer. Math. Soc. 132 (2004), 239-249 Request permission

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
  • MR Author ID: 328692
  • Email: nies@math.uchicago.edu, andre@cs.auckland.ac.nz
  • 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.
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 239-249
  • MSC (2000): Primary 03D25
  • DOI: https://doi.org/10.1090/S0002-9939-03-06984-3
  • MathSciNet review: 2021268