ArticleOriginal scientific text

Title

Wildness in the product groups

Authors 1

Affiliations

  1. 6363 MSB, Mathematics University of California at Los Angeles, Los Angeles, CA90095-1555, U.S.A.

Abstract

Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.

Keywords

group actions, Polish groups, group trees, product groups, permutation groups, Borel equivalence relations

Bibliography

  1. J. Barwise, Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Math. Logic, Springer, New York, 1975.
  2. H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge, 1996.
  3. H. Friedman and L. Stanley, A Borel reducibility theory for classes of structures, J. Symbolic Logic 54 (1989), 894-914.
  4. G. Hjorth, A universal Polish G-space, Topology Appl. 91 (1999), 141-150.
  5. J. W. Hungerford, Algebra, Grad. Texts in Math. 73, Springer, New York, 1974.
  6. A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, Berlin, 1995.
  7. M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 (1981), 301-318.
  8. M. Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267-294.
  9. S. Shelah, Refuting the Ehrenfeucht conjecture on rigid models, Israel J. Math. 25 (1976), 273-286.
  10. W. Sierpiński, Elementary Number Theory, North-Holland, Amsterdam, 1988.
  11. S. Solecki, Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995), 4765-4777.
  12. R. J. Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974/75) (collection of articles dedicated to Andrzej Mostowski on his sixtieth birthday), 269-294.
Pages:
1-33
Main language of publication
English
Received
1998-02-02
Accepted
1999-11-29
Published
2000
Exact and natural sciences