Algebra and Logic

, Volume 46, Issue 3, pp 163–187 | Cite as

The universal Lachlan semilattice without the greatest element

  • S. Yu. Podzorov
Article
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Abstract

We deal with some upper semilattices of m-degrees and of numberings of finite families. It is proved that the semilattice of all c.e. m-degrees, from which the greatest element is removed, is isomorphic to the semilattice of simple m-degrees, the semilattice of hypersimple m-degrees, and the semilattice of Σ 2 0 -computable numberings of a finite family of Σ 2 0 -sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.

Keywords

upper semilattice distributive semilattice m-degree numbering Rogers semilattice Lachlan semilattice 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • S. Yu. Podzorov
    • 1
  1. 1.Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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