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m-Degrees of supersets of simple sets

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Abstract

It is proved that there exists a simple, but not hypersimple, set A such that B ≤ A whenever A\( \subseteq \) B for every recursively enumerable set B.

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Literature cited

  1. A. H. Lachlan, “On the lattice of recursively enumerable sets,” Trans. Am. Math. Soc., 130, No. 1, 1–37 (1968).

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  2. A. H. Lachlan, “Two theorems on many-one degrees of recursively enumerable sets,” Algebra Logika, 11, No. 2, 216–226 (1972).

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Authors and Affiliations

  1. Tyumen State University, USSR

    A. N. Degtev

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  1. A. N. Degtev
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Translated from Matematicheskie Zametki, Vol. 23, No. 6, pp. 889–893, June, 1978.

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Degtev, A.N. m-Degrees of supersets of simple sets. Mathematical Notes of the Academy of Sciences of the USSR 23, 488–490 (1978). https://doi.org/10.1007/BF01431433

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  • DOI: https://doi.org/10.1007/BF01431433

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