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A high c.e. degree which is not the join of two minimal degrees. (English) Zbl 1216.03055

In this paper the author constructs a high c.e. degree which is not the join of two minimal degrees. The following result is obtained as a consequence of the proof: there exists a high c.e. degree \({\mathbf a}\) such that for any splitting of \({\mathbf a}\) into degrees \({\mathbf b}\) and \({\mathbf c}\), one of \({\mathbf b}\) or \({\mathbf c}\) bounds a \({\mathbf 1}\)-generic degree.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
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References:

[1] Recursion theory: its generalisation and applications (proceedings of Logic Colloquium ’79, Leeds) pp 52– (1980)
[2] Degrees of Unsolvabitity: Structure and Theory 759 (1979)
[3] DOI: 10.4153/CJM-1977-105-5 · Zbl 0355.02032
[4] Double jumps of minimal degrees 43 pp 715– (1978)
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