Abstract
We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees.
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The first author was supported by EPSRC Overseas Travel Grant No. EP/R006458/1.
The second author is a member of INDAM-GNSAGA.
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Shafer, P., Sorbi, A. Comparing the degrees of enumerability and the closed Medvedev degrees. Arch. Math. Logic 58, 527–542 (2019). https://doi.org/10.1007/s00153-018-0648-x
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DOI: https://doi.org/10.1007/s00153-018-0648-x