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Published online by Cambridge University Press: 12 March 2014
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
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