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  1. Some Effectively Infinite Classes of Enumerations.Sergey Goncharov, Alexander Yakhnis & Vladimir Yakhnis - 1993 - Annals of Pure and Applied Logic 60 (3):207-235.
    This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to strengthen the (...)
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  • On Injective Enumerability of Recursively Enumerable Classes of Cofinite Sets.Stephan Wehner - 1995 - Archive for Mathematical Logic 34 (3):183-196.
    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 (...)
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