Journal of Symbolic Logic

Equivalence structures and isomorphisms in the difference hierarchy

Douglas Cenzer, Geoffrey LaForte, and Jeffrey Remmel

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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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J. Symbolic Logic, Volume 74, Issue 2 (2009), 535-556.

First available in Project Euclid: 2 June 2009

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Cenzer, Douglas; LaForte, Geoffrey; Remmel, Jeffrey. Equivalence structures and isomorphisms in the difference hierarchy. J. Symbolic Logic 74 (2009), no. 2, 535--556. doi:10.2178/jsl/1243948326.

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