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June 2009 Equivalence structures and isomorphisms in the difference hierarchy
Douglas Cenzer, Geoffrey LaForte, Jeffrey Remmel
J. Symbolic Logic 74(2): 535-556 (June 2009). DOI: 10.2178/jsl/1243948326

Abstract

We examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak ω-c.e. categoricity, and that Δ02-categoricity is equivalent to our notion of graph-ω-c.e. categoricity.

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Douglas Cenzer. Geoffrey LaForte. Jeffrey Remmel. "Equivalence structures and isomorphisms in the difference hierarchy." J. Symbolic Logic 74 (2) 535 - 556, June 2009. https://doi.org/10.2178/jsl/1243948326

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

zbMATH: 1196.03049
MathSciNet: MR2518810
Digital Object Identifier: 10.2178/jsl/1243948326

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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