Geodesic
On some properties of the Medvedev lattice
Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 321-340

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This article investigates the structure of the lattice of degrees of difficulty, introduced by Medvedev. In particular, an answer is given to Rogers' question: Is being a degree of solvability a lattice-theoretic property? It is proved that for every degree except the smallest, the smallest nonrecursive, and the largest degrees, there exists a degree not comparable with it. Also analyzed are conditions under which there are no degrees lying strictly between two given degrees. The final consideration is a topological approach to certain questions about the structure of the Medvedev lattice. Bibliography: 2 titles. 
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     author = {E. Z. Dyment},
     title = {On some properties of the {Medvedev} lattice},
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E. Z. Dyment. On some properties of the Medvedev lattice. Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 321-340. http://geodesic.mathdoc.fr/item/SM_1976_30_3_a3/