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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 .

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

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