Abstract
We show that every nonzero \({\Delta^{0}_{2}}\) enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.
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Liliana Badillo and Andrea Sorbi would like to thank the Isaac Newton Institute for Mathematical Sciences of Cambridge, England, for its hospitality during the final phase this paper was completed. Hristo Ganchev and Andrea Sorbi were partially supported by the project Computability with partial information, sponsored by BNSF, Contract No: D002-258/18.12.08.
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Badillo, L., Bianchini, C., Ganchev, H. et al. A note on the enumeration degrees of 1-generic sets. Arch. Math. Logic 55, 405–414 (2016). https://doi.org/10.1007/s00153-015-0471-6
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DOI: https://doi.org/10.1007/s00153-015-0471-6