The ordertype of β-r.E. Sets

Journal of Symbolic Logic 55 (2):573-576 (1990)
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Let β be an arbitrary limit ordinal. A β-r.e. set is l-finite iff all its β-r.e. subsets are β-recursive. The l-finite sets correspond to the ideal of finite sets in the lattice of r.e. sets. We give a characterization of l-finite sets in terms of their ordertype: a β-r.e. set is l-finite iff it has ordertype less than β * , the Σ 1 projectum of β



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Ideals of Generalized Finite Sets in Lattices of Α-Recursively Enumerable Sets.Manuel Lerman - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):347-352.
Recursively Invariant Beta-Recursion Theory.Wolfgand Maass - 1981 - Annals of Mathematical Logic 21 (1):27.

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