Wildness in the product groups

• Autorzy: G. Hjorth
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 03E15: Descriptive set theory
• 03C15: Denumerable structures
• 20B35: Subgroups of symmetric groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 164
• Numer: 1
• Strony: 1-33

Daty

wydano

2000

otrzymano

1998-02-02

poprawiono

1999-11-29

Twórcy

autor

G. Hjorth

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

Bibliografia

• [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.