Effective categoricity of equivalence Structures

W. Calvert; D. Cenzer; V. S. Harizanov; A. Morozov

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arXiv · 0805.1887

Effective categoricity of equivalence Structures

W. Calvert·D. Cenzer·V. S. Harizanov·A. Morozov

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Abstract

An equivalence structure is a set with a single binary relation, satisfying sentences stating that the relation is an equivalence relation. A computable structure A is said to be $Δ^0_α$ categorical if for any computable structure B isomorphic to A there is a $Δ^0_α$ function witnessing that the two are isomorphic. The present paper gives an exact characterization of $Δ^0_α$ equivalence structures where $α= 1$ or $α\geq 3$. Extensive results for $α= 2$ are also given, and open cases are exhaustively described.

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BibTeX RIS

W. Calvert, D. Cenzer, V. S. Harizanov, A. Morozov. 2008-05-13. Effective categoricity of equivalence Structures. https://arxiv.org/abs/0805.1887

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