The minimal complementation property above 0′

Lewis-Pye, A. (2005). The minimal complementation property above 0′. Mathematical Logic Quarterly, 51(5), 470-492. https://doi.org/10.1002/malq.200410044
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Let us say that any (Turing) degree d > 0satisfies 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.

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