# Wildness in the product groups

Fundamenta Mathematicae (2000)

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

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topHjorth, 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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- [9] S. Shelah, Refuting the Ehrenfeucht conjecture on rigid models, Israel J. Math. 25 (1976), 273-286. Zbl0359.02053
- [10] W. Sierpiński, Elementary Number Theory, North-Holland, Amsterdam, 1988. Zbl0638.10001
- [11] S. Solecki, Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995), 4765-4777. Zbl0852.04003
- [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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