scholarly journals Locally Roelcke precompact Polish groups

2021 ◽  
Author(s):  
Joseph Zielinski
Keyword(s):  
Polish Groups

scholarly journals On Polish groups admitting non-essentially countable actions

2020 ◽  
pp. 1-15
Author(s):  
ALEXANDER S. KECHRIS ◽  
MACIEJ MALICKI ◽  
ARISTOTELIS PANAGIOTOPOULOS ◽  
JOSEPH ZIELINSKI
Keyword(s):  
Equivalence Relation ◽  
Isometry Group ◽  
Alternative Proof ◽  
Orbit Equivalence ◽  
Locally Compact ◽  
Continuous Action ◽  
Polish Groups ◽  
Infinite Dimensional ◽  
Open Question ◽  
New Criterion

Abstract It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.

scholarly journals AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES

2017 ◽  
Vol 82 (3) ◽  
pp. 1150-1179 ◽  
Author(s):  
TOMÁS IBARLUCÍA
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Original Structure ◽  
Polish Groups ◽  
Separable Models

AbstractWe study automorphism groups of randomizations of separable structures, with focus on the ℵ0-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the ℵ0-categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banach-theoretic translation. Finally, we study and classify the separable models of the theory of beautiful pairs of randomizations, showing in particular that this theory is never ℵ0-categorical (except in basic cases).

scholarly journals Polish groups and Baire category methods

2016 ◽  
Vol 8 (1) ◽  
pp. 89-164 ◽  
Author(s):  
Julien Melleray
Keyword(s):  
Baire Category ◽  
Polish Groups

Ethnic identity of representatives of the Ukrainian minority university students in Poland

2021 ◽  
Vol 64 (21) ◽  
pp. 58-69
Author(s):  
Krzysztof Zegar ◽  
Maria Łoskot ◽  
Julia Pierzyńska ◽  
Małgorzata Siemiątkowska
Keyword(s):  
Decision Making ◽  
Ethnic Identity ◽  
National Identity ◽  
International Students ◽  
Social Identity ◽  
Identity Development ◽  
Narrative Analysis ◽  
Social Issues ◽  
Polish Groups ◽  
Self Confidence

Introduction: Referring to the knowledge about the number of Ukrainian students in Poland, James Marcia’s theory of identity development and Henri Tajfel’s theory of social identity, the authors examined how the Ukrainian minority studying in Poland describes its ethnic identity. Method: For this purpose, nine semistructural interviews were conducted, which were then subjected to a semantic narrative analysis. Results: It turned out that the respondents identify most strongly with the group of international students and students, and with their national identity in the second place. Polish nationality was cited as a group of belonging, spending time, while the Ukrainian nationality was individual, related to origin. Polish groups were positively evaluated by the respondents. The analysis also distinguished categories of differences between Poland and Ukraine, indicated by the respondents. They were: culture and religion, customs and tradition, decision-making and self-confidence, social issues, as well as mentality and science. The categories of stereotypes that were mentioned in the interviews were also identified: cheating and stealing, complaining and the similarity of nations. Conclusions: The results showed that the identity of Ukrainians is in a state of moratorium. The respondents define Ukraine as “their” country, while the strongest ones describe themselves as international students.

A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group

2006 ◽  
Vol 71 (4) ◽  
pp. 1108-1124 ◽  
Author(s):  
Alex Thompson
Keyword(s):  
Equivalence Relation ◽  
Polish Space ◽  
Invariant Metrics ◽  
Orbit Equivalence ◽  
Invariant Metric ◽  
Continuous Action ◽  
Polish Groups ◽  
Polish Group ◽  
Left Invariant Metrics

AbstractStrengthening a theorem of Hjorth this paper gives a new characterization of which Polish groups admit compatible complete left invariant metrics. As a corollary it is proved that any Polish group without a complete left invariant metric has a continuous action on a Polish space whose associated orbit equivalence relation is not essentially countable.

Splitting and representation groups for Polish groups

1978 ◽  
Vol 19 (2) ◽  
pp. 452-460 ◽  
Author(s):  
U. Cattaneo
Keyword(s):  
Polish Groups

scholarly journals Borel actions of Polish groups

1993 ◽  
Vol 28 (2) ◽  
pp. 334-342 ◽  
Author(s):  
Howard Becker ◽  
Alexander S. Kechris
Keyword(s):  
Polish Groups
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