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Degrees of categoricity of computable structures

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Abstract

Defining the degree of categoricity of a computable structure \({\mathcal{M}}\) to be the least degree d for which \({\mathcal{M}}\) is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).

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Authors and Affiliations

  1. Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, 1090, Vienna, Austria

    Ekaterina B. Fokina

  2. N.G. Chebotarev Research Institute of Mechanics and Mathematics, Kazan State University, Universitetskaya St. 17, 420008, Kazan, Russia

    Iskander Kalimullin

  3. Department of Mathematics, Queens College, C.U.N.Y., 65-30 Kissena Blvd., Flushing, NY, 11367, USA

    Russell Miller

  4. Ph.D. Programs in Computer Science and Mathematics, The Graduate Center of C.U.N.Y., 365 Fifth Avenue, New York, NY, 10016, USA

    Russell Miller

Authors
  1. Ekaterina B. Fokina
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  2. Iskander Kalimullin
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  3. Russell Miller
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Corresponding author

Correspondence to Ekaterina B. Fokina.

Additional information

E. B. Fokina was partially supported by the Russian Foundation for Basic Research (grant RFBR 08-01-00336) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (grant NSh-335.2008.1.). All three authors were supported by binational grant # DMS 0554841 from the National Science Foundation. The main question discussed in this paper was suggested by Sergey Goncharov.

I. Kalimullin was partially supported by the Russian Foundation for Basic Research (grant RFBR 05-01-00605) and RF President grant MK-4314.2008.1.

R. Miller was partially supported by grants numbered 80209-04 12, 67182-00-36, 68470-00 37, 69723-00 38, and 61467-00 39 from The City University of New York PSC-CUNY Research Award Program, and by grant #13397 from the Templeton Foundation.

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Fokina, E.B., Kalimullin, I. & Miller, R. Degrees of categoricity of computable structures. Arch. Math. Logic 49, 51–67 (2010). https://doi.org/10.1007/s00153-009-0160-4

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  • DOI: https://doi.org/10.1007/s00153-009-0160-4

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