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The ordertype of β-R.E. sets
Published online by Cambridge University Press: 12 March 2014
Abstract
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 Σ1, projectum of β).
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- Copyright © Association for Symbolic Logic 1990
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REFERENCES
[1]Devlin, K. J., Aspects of constructibility, Lecture Notes in Mathematics, vol. 354, Springer-Verlag, Berlin, 1973.CrossRefGoogle Scholar
[2]Lerman, M., Congruence relations, filters, ideals and definability in lattices of α-r.e. sets, this Journal, vol. 41 (1976), pp. 405–418.Google Scholar
[3]Lerman, M., Ideals of generalized finite sets in the lattice of α-r.e. sets, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 22 (1976), pp. 347–352.CrossRefGoogle Scholar
[4]Friedman, S. D., β-recursion theory, Transactions of the American Mathematical Society, vol. 255 (1979), pp. 173–200.Google Scholar
[5]Friedman, S. D., Post's problem without admissibility, Advances in Mathematics, vol. 35 (1980), pp. 30–49.CrossRefGoogle Scholar
[7]Maass, W., Recursively invariant β-recursion theory, Annals of Mathematical Logic, vol. 21 (1981), pp. 27–73.CrossRefGoogle Scholar