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


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 .


Distributive Lattice Medvedev Degree Muchnik Lattice Medvedev Reducibility Countable Distributive Lattice 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUSA

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