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Equivalence structures and isomorphisms in the difference hierarchy

  • Douglas Cenzer (a1), Geoffrey Laforte (a2) and Jeffrey Remmel (a3)

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.

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[1]Calvert, W., Cenzer, D., Harizanov, V., and Morozov, A., Effective categoricity of equivalence structures, Annals of Pure and Applied Logic, vol. 141 (2006), pp. 6178.
[2]Khisamiev, N. G., Constructive abelian p-groups, Siberian Advances in Mathematics, vol. 2 (1992), pp. 68113.
[3]Khoussainov, B., Stephan, F., and Yang, Y., Computable categoricity and the Ershov hierarchy, unpublished.
[4]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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