Studia Logica

, Volume 67, Issue 1, pp 27–59 | Cite as

Computably Enumerable Equivalence Relations

  • Su Gao
  • Peter Gerdes


We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.

computably enumerable sets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Becker, H., and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Mathematical Society Lecture Note Serious 232, Cambridge University Press, 1996.Google Scholar
  2. [2]
    Bernardi, C., and A. Sorbi, 'Classifying positive equivalence relations', J.Sym bolic Logic 48 (1983), 529-538.Google Scholar
  3. [3]
    Ershov, Yu. L., 'Positive equivalence relations' (English translation), Algebra and Logic 10 (1973), 378-394.Google Scholar
  4. [4]
    Friedman, H., and L. Stanley, 'A Borel reducibility theory for classes of countable structures', J.Sym bolic Logic 54 (1989), 894-914.Google Scholar
  5. [5]
    Lachlan, A.H., 'A note on positive equivalence relations', Zeitschr. f. math. Logik und Grundlagen d. Math. 33 (1987), 43-46.Google Scholar
  6. [6]
    Miller, C.F., III, On Group-theoretic Decision Problems and Their Classification, Annals of Mathematics Studies, No. 68, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1971.Google Scholar
  7. [7]
    Nies, A., 'Computably enumerable equivalence relations modulo finite differences', Math. Log. Quart. 40 (1994), 490-518.Google Scholar
  8. [8]
    Rabin, M.O., 'Computable unsolvability of group theoretic problems', Ann. Math. 67 (1958), 172-194.Google Scholar
  9. [9]
    Rogers, H., Theory of Computable Functions and Effective Computability, MIT Press, 1987.Google Scholar
  10. [10]
    Visser, A., 'Numerations, lambda-calculus and arithmetic', in To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (J.P. Seldin and J.R. Hindley, eds.), Academic Press, New York, 1980, 259-284.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Su Gao
    • 1
  • Peter Gerdes
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadena

Personalised recommendations