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Isolated 2-computably enumerable Q-degrees

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Abstract

In this work we prove that for every pair of computably enumerable degrees a<Q b there exists a properly 2-computably enumerable degree d such that a <Q d <Q b, a isolates d from below, and b isolates d from above. Two corollaries follow from this result. First, there exists a 2-computably enumerable degree which is Q-incomparable with any nontrivial (different from 0 and 0′) computably enumerable degree. Second, every nontrivial computably enumerable degree isolates some 2-computably enumerable degree from below and some 2-computably enumerable degree from above.

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Authors and Affiliations

  1. Kazan State University, 18 Kremlevskaya str., Kazan, 420008, Russia

    I.I. Batyrshin

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  1. I.I. Batyrshin
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Correspondence to I.I. Batyrshin.

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Original Russian Text © I.I.Batyrshin, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 4, pp. 3–9.

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Batyrshin, I. Isolated 2-computably enumerable Q-degrees. Russ Math. 54, 1–6 (2010). https://doi.org/10.3103/S1066369X10040018

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  • DOI: https://doi.org/10.3103/S1066369X10040018

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