The minimal complementation property above 0′

Mathematical Logic Quarterly 51 (5):470-492 (2005)
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Abstract

Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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10.1002/malq.200410044

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References found in this work

Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.
Minimal degrees and the jump operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
A theorem on minimal degrees.J. R. Shoenfield - 1966 - Journal of Symbolic Logic 31 (4):539-544.
The upper semilattice of degrees ≤ 0' is complemented.David B. Posner - 1981 - Journal of Symbolic Logic 46 (4):705 - 713.

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