Splittings of 0' into the Recursively Enumerable Degrees

Mathematical Logic Quarterly 42 (1):249-269 (1996)
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Abstract

Lachlan [9] proved that there exists a non-recursive recursively enumerable degree such that every non-recursive r. e. degree below it bounds a minimal pair. In this paper we first prove the dual of this fact. Second, we answer a question of Jockusch by showing that there exists a pair of incomplete r. e. degrees a0, a1 such that for every non-recursive r. e. degree w, there is a pair of incomparable r. e. degrees b0, b2 such that w = b0 V b1 and bi for i = 0, 1

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References found in this work

A minimal pair of recursively enumerable degrees.C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (2):159-168.
Bounding minimal pairs.A. H. Lachlan - 1979 - Journal of Symbolic Logic 44 (4):626-642.
Highness and bounding minimal pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.

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