ArticleOriginal scientific text

Title

A dichotomy theorem for mono-unary algebras

Authors 1

Affiliations

  1. Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, U.S.A.

Abstract

We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.

Keywords

descriptive set theory, countable model theory, admissible set theory

Bibliography

  1. [Ba] J. Barwise, Admissible Sets and Structures: an Approach to Definability Theory, Perspectives in Math. Logic, Springer, Berlin, 1975.
  2. [BK] H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge Univ. Press, Cambridge, 1996.
  3. [FS] H. Friedman and L. Stanley, A Borel reducibility theory for classes of countable structures, J. Symbolic Logic 54 (1989), 894-914.
  4. [Ga] S. Gao, The isomorphism relation between countable models and definable equivalence relations, Ph.D. dissertation, UCLA, 1998.
  5. [HKL] L. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928.
  6. [HK] G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273-1300.
  7. [Ma] L. Marcus, The number of countable models of a theory of one unary function, Fund. Math. 58 (1980), 171-181.
  8. [Sa] R. Sami, Polish group actions and the Vaught Conjecture, Trans. Amer. Math. Soc. 341 (1994), 335-353.
  9. [St] J. R. Steel, On Vaught's Conjecture, in: Cabal Seminar 76-77, Lecture Notes in Math. 689, Springer, Berlin, 1978, 193-208.
Pages:
25-37
Main language of publication
English
Received
1999-03-02
Accepted
1999-09-07
Published
2000
Exact and natural sciences