Authors: Farah, Ilijas 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Basis problem for turbulent actions I: Tsirelson submeasures
Journal: Annals of Pure and Applied Logic
Volume: 108
Issue: 1-3
First page: 189
Last page: 203
Issue Date: 30-Mar-2001
Rank: M21
ISSN: 0168-0072
DOI: 10.1016/S0168-0072(00)00045-2
Abstract: 
We use modified Tsirelson's spaces (Casazza and Shura, Lecture Notes in Mathematics, Vol. 1363, Springer, Berlin, 1980) to prove that there is no finite basis for turbulent Polish group actions. This answers a question of Hjorth and Kechris (see Hjorth and Kechris, Bull. Symbolic Logic 3 (1997) 329-346; Hjorth, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2000, Section 3.4.3).
Keywords: Borel equivalence relations | Tsirelson space
Publisher: Elsevier

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