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Equivalence structures and isomorphisms in the difference hierarchy

Published online by Cambridge University Press:  12 March 2014

Douglas Cenzer ,
Geoffrey Laforte  and
Jeffrey Remmel
Douglas Cenzer
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA, E-mail: cenzer@math.ufl.edu
Geoffrey Laforte
Affiliation:
Department of Mathematics and Statistics, University of West Florida, Pensacola, Fl 32514, USA, E-mail: glaforte@uwf.edu
Jeffrey Remmel
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, Ca 92093-0112, USA, E-mail: jremmel@ucsd.edu
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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 -categoricity is equivalent to our notion of graph-ω-c.e. categoricity.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 535 - 556
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

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