Annals of Pure and Applied Logic 62 (3):207-263 (1993)

Abstract
This paper analyzes several properties of infima in Dn, the n-r.e. degrees. We first show that, for every n> 1, there are n-r.e. degrees a, b, and c, and an -r.e. degree x such that a < x < b, c and, in Dn, b c = a. We also prove a related result, namely that there are two d.r.e. degrees that form a minimal pair in Dn, for each n < ω, but that do not form a minimal pair in Dω. Next, we show that every low r.e. degree branches in the d.r.e. degrees. This result does not extend to the low2 r.e. degrees. We also construct a non-low r.e. degree a such that every r.e. degree b a branches in the d.r.e. degrees. Finally we prove that the nonbranching degrees are downward dense in the d.r.e. degrees
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DOI 10.1016/0168-0072(93)90238-9
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References found in this work BETA

The D.R.E. Degrees Are Not Dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
A Minimal Pair of Recursively Enumerable Degrees.C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (2):159-168.
The Density of Infima in the Recursively Enumerable Degrees.Theodore A. Slaman - 1991 - Annals of Pure and Applied Logic 52 (1-2):155-179.

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Citations of this work BETA

Infima of D.R.E. Degrees.Jiang Liu, Shenling Wang & Guohua Wu - 2010 - Archive for Mathematical Logic 49 (1):35-49.

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