Journal of Symbolic Logic

Equivalence structures and isomorphisms in the difference hierarchy

Douglas Cenzer, Geoffrey LaForte, and Jeffrey Remmel

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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.

Article information

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

Dates
First available in Project Euclid: 2 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1243948326

Digital Object Identifier
doi:10.2178/jsl/1243948326

Mathematical Reviews number (MathSciNet)
MR2518810

Zentralblatt MATH identifier
1196.03049

Citation

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. https://projecteuclid.org/euclid.jsl/1243948326


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