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Archive for Mathematical Logic

, Volume 43, Issue 3, pp 399–414 | Cite as

Embeddings into the Medvedev and Muchnik lattices of Π0 1 classes

  • Stephen Binns
  • Stephen G. Simpson
Article

Abstract.

Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Π1 0 subsets of 2ω, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w . We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M .

Keywords

Distributive Lattice Medvedev Degree Muchnik Lattice Medvedev Reducibility Countable Distributive Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUSA

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