Journal of Symbolic Logic

On the Orbits of Hyperhypersimple Sets

Wolfgang Maass

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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 $\Sigma^0_3$-definable isomorphism between their lattices of supersets. Lerman, Shore and Soare have shown that this is not true if one replaces $\Sigma^0_3$ by $\Sigma^0_4$.

Article information

Source
J. Symbolic Logic, Volume 49, Issue 1 (1984), 51-62.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741474

Mathematical Reviews number (MathSciNet)
MR736602

Zentralblatt MATH identifier
0579.03027

JSTOR
links.jstor.org

Citation

Maass, Wolfgang. On the Orbits of Hyperhypersimple Sets. J. Symbolic Logic 49 (1984), no. 1, 51--62. https://projecteuclid.org/euclid.jsl/1183741474


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