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 $\mathcal {E}_\Pi$.References
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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