Embeddings into the Medvedev and Muchnik lattices of Π1 classes
نویسندگان
چکیده
Let Pw and PM be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Π1 subsets of 2 , under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of Pw. We show that many countable distributive lattices are lattice-embeddable below any non-zero element of PM .
منابع مشابه
Small Π 01 Classes . Stephen Binns
The property of smallness for Π1 classes is introduced and is investigated with respect to Medvedev and Muchnik degree. It is shown that the property of containing a small Π1 class depends only on the Muchnik degree of a Π1 class. A comparison is made with the idea of thinness for Π1 classes
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