Wildness in the product groups
Hjorth, G.
Fundamenta Mathematicae, Tome 163 (2000), p. 1-33 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212445 
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     pages = {1-33},
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Hjorth, G. Wildness in the product groups. Fundamenta Mathematicae, Tome 163 (2000) pp. 1-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv164i1p1bwm/

[00000] [1] J. Barwise, Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Math. Logic, Springer, New York, 1975. | Zbl 0316.02047

[00001] [2] H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge, 1996. | Zbl 0949.54052

[00002] [3] H. Friedman and L. Stanley, A Borel reducibility theory for classes of structures, J. Symbolic Logic 54 (1989), 894-914. | Zbl 0692.03022

[00003] [4] G. Hjorth, A universal Polish G-space, Topology Appl. 91 (1999), 141-150.

[00004] [5] J. W. Hungerford, Algebra, Grad. Texts in Math. 73, Springer, New York, 1974.

[00005] [6] A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, Berlin, 1995.

[00006] [7] M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 (1981), 301-318. | Zbl 0501.03018

[00007] [8] M. Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267-294. | Zbl 0301.02050

[00008] [9] S. Shelah, Refuting the Ehrenfeucht conjecture on rigid models, Israel J. Math. 25 (1976), 273-286. | Zbl 0359.02053

[00009] [10] W. Sierpiński, Elementary Number Theory, North-Holland, Amsterdam, 1988. | Zbl 0638.10001

[00010] [11] S. Solecki, Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995), 4765-4777. | Zbl 0852.04003

[00011] [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.