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On the existence of a strong minimal pair
Journal of Mathematical Logic 15 (1):1550003 (2015)
Abstract
We show that there is a strong minimal pair in the computably enumerable Turing degrees, i.e. a pair of nonzero c.e. degrees a and b such that a∩b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.Author's Profile
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Citations of this work
Mass problems and density.Stephen Binns, Richard A. Shore & Stephen G. Simpson - 2016 - Journal of Mathematical Logic 16 (2):1650006.
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.
Working below a high recursively enumerable degree.Richard A. Shore & Theodore A. Slaman - 1993 - Journal of Symbolic Logic 58 (3):824-859.
Lattice embeddings into the recursively enumerable degrees.K. Ambos-Spies & M. Lerman - 1986 - Journal of Symbolic Logic 51 (2):257-272.
Non-bounding constructions.J. R. Shoenfield - 1990 - Annals of Pure and Applied Logic 50 (2):191-205.
A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees.M. Lerman - 2000 - Annals of Pure and Applied Logic 101 (2-3):275-297.
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