Abstract
To date the problem of finding a general characterization of injective enumerability of recursively enumerable (r.e) classes of r.e. sets has proved intractable. This paper investigates the problem for r.e. classes of cofinite sets. We state a suitable criterion for r.e. classesC such that there is a boundn∈ω with |ω-A|≤n for allA∈C. On the other hand an example is constructed which shows that Lachlan's condition (F) does not imply injective enumerability for r.e. classes of cofinite sets. We also look at a certain embeddability property and show that it is equivalent with injective enumerability for certain classes of cofinite sets. At the end we present a reformulation of property (F).
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Thank you for technical support, Wolfgang Eppler, for intellectual support, Alistair Lachlan, and for proof-reading, Martin Kummer. Thanks also to the anonymous referee
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Wehner, S. On injective enumerability of recursively enumerable classes of cofinite sets. Arch Math Logic 34, 183–196 (1995). https://doi.org/10.1007/BF01375520
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DOI: https://doi.org/10.1007/BF01375520