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Density of the Medvedev lattice of Π0 1 classes

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Abstract.

The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, Fl, 32611-8105, USA

    Douglas Cenzer

  2. Department of Mathematics, University of Michigan, 2072 East Hall, Ann Arbor, MI, 48109-1109, USA

    Peter G. Hinman

Authors
  1. Douglas Cenzer
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  2. Peter G. Hinman
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Correspondence to Douglas Cenzer.

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Mathematics Subject Classification (2000): 03D30, 03D25

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Cenzer, D., Hinman, P. Density of the Medvedev lattice of Π0 1 classes. Arch. Math. Logic 42, 583–600 (2003). https://doi.org/10.1007/s00153-002-0166-7

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  • DOI: https://doi.org/10.1007/s00153-002-0166-7

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