scholarly journals Glasner’s problem for Polish groups with metrizable universal minimal flow

2019 ◽  
Vol 69 (2) ◽  
pp. 941-953
Author(s):  
Lionel Nguyen Van Thé
Keyword(s):  
Minimal Flow ◽  
Polish Groups

scholarly journals Maximally highly proximal flows

2020 ◽  
pp. 1-21 ◽  
Author(s):  
ANDY ZUCKER
Keyword(s):  
Structure Theorem ◽  
Dynamical Behavior ◽  
Minimal Flow ◽  
Complete Structure ◽  
Polish Groups ◽  
Polish Group

For $G$ a Polish group, we consider $G$ -flows which either contain a comeager orbit or have all orbits meager. We single out a class of flows, the maximally highly proximal (MHP) flows, for which this analysis is particularly nice. In the former case, we provide a complete structure theorem for flows containing comeager orbits, generalizing theorems of Melleray, Nguyen Van Thé, and Tsankov and of Ben Yaacov, Melleray, and Tsankov. In the latter, we show that any minimal MHP flow with all orbits meager has a metrizable factor with all orbits meager, thus ‘reflecting’ complicated dynamical behavior to metrizable flows. We then apply this to obtain a structure theorem for Polish groups whose universal minimal flow is distal.

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).

End-tidal control vs. manually controlled minimal-flow anesthesia: a prospective comparative trial

2017 ◽  
Vol 61 (10) ◽  
pp. 1262-1269 ◽  
Author(s):  
A. J. Wetz ◽  
M. M. Mueller ◽  
K. Walliser ◽  
C. Foest ◽  
S. Wand ◽  
...  
Keyword(s):  
Comparative Trial ◽  
Minimal Flow ◽  
End Tidal

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
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