Isomorphisms of splits of computably enumerable sets

We show that if A and$\widehat{A}$are automorphic via Φ then the structures$S_{R}(A)$and$S_{R}(\widehat{A})$are$\Delta_{3}^{0}-isomorphic$via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.

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Bibliographic Details
Published in:The Journal of symbolic logic 2003-09, Vol.68 (3), p.1044-1064
Main Authors: Cholak, Peter A., Harrington, Leo A.
Format: Article
Language:English
Subjects:
03D25
Approximation
Automorphisms
Boolean algebras
Integers
Logical proofs
Logical theorems
Low earth orbits
Mathematical functions
Mathematical logic
Mathematical theorems
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Description
Summary:We show that if A and$\widehat{A}$are automorphic via Φ then the structures$S_{R}(A)$and$S_{R}(\widehat{A})$are$\Delta_{3}^{0}-isomorphic$via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
ISSN:0022-4812
1943-5886
DOI:10.2178/jsl/1058448453