Abstract
It is shown that for every Turing degree d there is an ω-categorical group G such that the isomorphism type of G is of degree d. We also find an ω-categorical group G such that the isomorphism type of G has no degree.
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Ivanov, A. Degrees of isomorphism types and countably categorical groups. Arch. Math. Logic 51, 93–98 (2012). https://doi.org/10.1007/s00153-011-0255-6
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DOI: https://doi.org/10.1007/s00153-011-0255-6