Properly Σ2 minimal degrees and 0″ complementation

Cooper, S. Barry; Lewis-Pye, Andrew; and Yang, Yue (2005) Properly Σ2 minimal degrees and 0″ complementation. Mathematical Logic Quarterly, 51 (3). pp. 274-276. ISSN 0942-5616
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We show that there exists a properly Σ2 minimal (Turing) degree b, and moreover that b can be chosen to join with 0′ to 0″ – so that b is a 0″ complement for every degree a such that 0′ ≤ a < 0″.

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