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On the orbits of hyperhypersimple sets

Published online by Cambridge University Press:  12 March 2014

Wolfgang Maass
Wolfgang Maass*
Affiliation:
University of Illinois at Chicago, Chicago, Illinois 60680
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Abstract

This paper contributes to the question of under which conditions recursively enumerable sets with isomorphic lattices of recursively enumerable-supersets are automorphic in the lattice of all recursively enumerable sets. We show that hyperhypersimple sets (i.e. sets where the recursively enumerable supersets form a Boolean algebra) are automorphic if there is a -definable isomorphism between their lattices of supersets. Lerman, Shore and Soare have shown that this is not true if one replaces by .

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 1 , March 1984 , pp. 51 - 62
Copyright
Copyright © Association for Symbolic Logic 1984

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References

REFERENCES

[1]Lachlan, A. H., On the lattice of recursively enumerable sets, Transactions of the American Mathematical Society, vol. 130 (1968), pp. 1–37.CrossRefGoogle Scholar
[2]Lerman, M., Shore, R. A. and Soare, R. I., r-maximal major subsets, Israel Journalof Mathematics, vol. 31 (1978), pp. 1–18.CrossRefGoogle Scholar
[3]Maass, W., Characterization of recursively enumerable sets with supersets effectively isomorphic to all recursively enumerable sets, Transactions of the American Mathematical Society, vol. 279 (1983), pp. 311–336.CrossRefGoogle Scholar
[4]Martin, D. A., Classes of recursively enumerable sets and degrees of unsolvability, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik, vol. 12 (1966), pp. 295–310.CrossRefGoogle Scholar
[5]Soare, R. I., Automorphisms of the lattice of recursively enumerable sets. Part I: Maximal sets, Annals of Mathematics, ser. 2, vol. 100 (1974), pp. 80–120.CrossRefGoogle Scholar
[6]Soare, R. I., Computational complexity, speedable and levelable sets, this Journal, vol. 42 (1977), pp. 545–563.Google Scholar
[7]Soare, R. I., Recursively enumerable sets and degrees, Bulletin of the American Mathematical Society, vol. 84 (1978), pp. 1149–1181.CrossRefGoogle Scholar