Wildness in the product groups

G. Hjorth

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 1, page 1-33
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Hjorth, G.. "Wildness in the product groups." Fundamenta Mathematicae 164.1 (2000): 1-33. <http://eudml.org/doc/212445>.

@article{Hjorth2000,
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.},
author = {Hjorth, G.},
journal = {Fundamenta Mathematicae},
keywords = {group actions; Polish groups; group trees; product groups; permutation groups; Borel equivalence relations; continuous group actions; nonabelian Polish groups; tame groups},
language = {eng},
number = {1},
pages = {1-33},
title = {Wildness in the product groups},
url = {http://eudml.org/doc/212445},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Hjorth, G.
TI - Wildness in the product groups
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 1
SP - 1
EP - 33
AB - 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.
LA - eng
KW - group actions; Polish groups; group trees; product groups; permutation groups; Borel equivalence relations; continuous group actions; nonabelian Polish groups; tame groups
UR - http://eudml.org/doc/212445
ER -

References

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  1. [1] J. Barwise, Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Math. Logic, Springer, New York, 1975. Zbl0316.02047
  2. [2] H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge, 1996. Zbl0949.54052
  3. [3] H. Friedman and L. Stanley, A Borel reducibility theory for classes of structures, J. Symbolic Logic 54 (1989), 894-914. Zbl0692.03022
  4. [4] G. Hjorth, A universal Polish G-space, Topology Appl. 91 (1999), 141-150. 
  5. [5] J. W. Hungerford, Algebra, Grad. Texts in Math. 73, Springer, New York, 1974. 
  6. [6] A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, Berlin, 1995. 
  7. [7] M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 (1981), 301-318. Zbl0501.03018
  8. [8] M. Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267-294. Zbl0301.02050
  9. [9] S. Shelah, Refuting the Ehrenfeucht conjecture on rigid models, Israel J. Math. 25 (1976), 273-286. Zbl0359.02053
  10. [10] W. Sierpiński, Elementary Number Theory, North-Holland, Amsterdam, 1988. Zbl0638.10001
  11. [11] S. Solecki, Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995), 4765-4777. Zbl0852.04003
  12. [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. 

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