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Embeddings into the Medvedev and Muchnik lattices of Π0 1 classes

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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 .

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, McAllister Building, University Part, PA 16802, USA

    Stephen Binns & Stephen G. Simpson

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  1. Stephen Binns
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  2. Stephen G. Simpson
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Correspondence to Stephen Binns.

Additional information

Simpson’s research was partially supported by NSF Grant DMS-0070718. We thank the anonymous referee for a careful reading of this paper and helpful comments.

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Binns, S., Simpson, S. Embeddings into the Medvedev and Muchnik lattices of Π0 1 classes. Arch. Math. Logic 43, 399–414 (2004). https://doi.org/10.1007/s00153-003-0195-x

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