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Topological aspects of the Medvedev lattice

✍ Scribed by Andrew E. M. Lewis; Richard A. Shore; Andrea Sorbi

Publisher: Springer
Year: 2010
Tongue: English
Weight: 266 KB
Volume: 50
Category: Article
ISSN: 0933-5846
DOI: 10.1007/s00153-010-0215-6

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## Abstract This is a contribution to the study of the Muchnik and Medvedev lattices of non‐empty Π^0^~1~ subsets of 2^__ω__^. In both these lattices, any non‐minimum element can be split, i. e. it is the non‐trivial join of two other elements. In fact, in the Medvedev case, if__P__ > ~M~ __Q__, th