David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 65 (4):1881-1894 (2000)
We show that each non-compact Polish group admits a continuous action on a Polish space with non-smooth orbit equivalence relation. We actually construct a free such action. Thus for a Polish group compactness is equivalent to all continuous free actions of this group being smooth. This answers a question of Kechris. We also establish results relating local compactness of the group with its inability to induce orbit equivalence relations not reducible to countable Borel equivalence relations. Generalizing a result of Hjorth, we prove that each non-locally compact, that is, infinite dimensional, separable Banach space has a continuous action on a Polish space with non-Borel orbit equivalence relation, thus showing that this property characterizes non-local compactness among Banach spaces
|Keywords||Polish Group Continuous Action Orbit Equivalence Relation|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Arthur W. Apter (1981). Measurability and Degrees of Strong Compactness. Journal of Symbolic Logic 46 (2):249-254.
Kenneth Schilling & Boško Živaljević (1997). Louveau's Theorem for the Descriptive Set Theory of Internal Sets. Journal of Symbolic Logic 62 (2):595-607.
Arthur W. Apter (1999). On Measurable Limits of Compact Cardinals. Journal of Symbolic Logic 64 (4):1675-1688.
Dale Radin (2004). A Definability Result for Compact Complex Spaces. Journal of Symbolic Logic 69 (1):241-254.
Christian Rosendal (2005). Cofinal Families of Borel Equivalence Relations and Quasiorders. Journal of Symbolic Logic 70 (4):1325-1340.
Renling Jin & Saharon Shelah (1998). Compactness of Loeb Spaces. Journal of Symbolic Logic 63 (4):1371-1392.
Asger Törnquist (2006). Orbit Equivalence and Actions of Fn. Journal of Symbolic Logic 71 (1):265 - 282.
Longyun Ding & Su Gao (2006). Diagonal Actions and Borel Equivalence Relations. Journal of Symbolic Logic 71 (4):1081 - 1096.
Alex Thompson (2006). A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group. Journal of Symbolic Logic 71 (4):1108 - 1124.
Added to index2009-01-28
Total downloads11 ( #312,411 of 1,906,946 )
Recent downloads (6 months)3 ( #277,342 of 1,906,946 )
How can I increase my downloads?