Basis problem for turbulent actions I: Tsirelson submeasures Original Research Article

We use modified Tsirelsonʹs 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).