Abstract.
Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in Ishmukhametov [1999] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least elementm \(>\) 0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that for any REA-degree d below 0 \('\) the class Q[d] cannot have a least element and more generally is not bounded below by a non-zero degree, except in the trivial cases.
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Received: 17 January 1996
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Ishmukhametov, S. On relative enumerability of Turing degrees. Arch Math Logic 39, 145–154 (2000). https://doi.org/10.1007/s001530050139
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DOI: https://doi.org/10.1007/s001530050139