Isomorphism of Lattices of Recursively Enumerable Sets

Abstract

Let ω = { 0, 1, 2, . . . }, and for A ⊆ ω, let EA be the lattice of subsets of ω which are recursively enumerable relative to the “oracle” A. Let (EA)∗ be EA/I, where I is the ideal of finite subsets of ω. It is established that for any A,B ⊆ ω, (EA)∗ is effectively isomorphic to (EB)∗ if and only if A′ ≡T B′, where A′ is the Turing jump of A. A consequence… (More)

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Cite this paper

@inproceedings{Hammond1997IsomorphismOL, title={Isomorphism of Lattices of Recursively Enumerable Sets}, author={T E Hammond}, year={1997} }