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Orbits of hyperhypersimple sets and the lattice of Σ03 sets

Published online by Cambridge University Press:  12 March 2014

E. Herrmann*
Affiliation:
Humboldt-Universität, 1086 Berlin, Postfach 1297, Deutsche Demokratisch Republik

Abstract

It will be shown that in the lattice of recursively enumerable sets all lattices L3(X) are elementarily definable with parameters, where X is and L3(X) consists of all sets containing X.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1983

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References

REFERENCES

[1]Herrmann, E., Der Verband der rekursiv aufzählbaren Mengen, Seminarbericht, vol. 10, Humboldt-Universität, Berlin, 1978.Google Scholar
[2]Herrmann, E., Major Untermengen von hyperhypersimplen Mengen und Idealfamilien (to appear).Google Scholar
[3]Lachlan, A.H., On the lattice of recursively enumerable sets, Transactions of the American Mathematical Society, vol. 130 (1968), pp. 137.CrossRefGoogle Scholar
[4]Lerman, M., Shore, R.A. and Soare, R.I., R-maximal major subsets, Israel Journal of Mathematics, vol. 31 (1978), pp. 118.CrossRefGoogle Scholar
[5]Lerman, M. and Soare, R.I., A decidable fragment of the elementary theory of the lattice of recursively enumerable sets, Transactions of the American Mathematical Society, vol. 257 (1980), pp. 137.CrossRefGoogle Scholar
[6]Rogers, H., Theory of recursive functions and effective computahility, McGraw-Hill, New York, 1967.Google Scholar
[7]Soare, R.I., Recursively enumerable sets and degrees, Bulletin of the American Mathematical Society, vol. 84 (1978), pp. 11491181.CrossRefGoogle Scholar