6 papers
Big Ramsey Degrees in Ultraproducts of Finite Structures
Dana Bartošová, Mirna Džamonja, Rehana Patel +1
We develop a transfer principle of structural Ramsey theory from finite structures to ultraproducts. We show that under certain mild conditions, when a class of finite structures h…
A new perspective on semi-retractions and the Ramsey property
Dana Bartošová, Lynn Scow
We investigate the notion of a semi-retraction between two first order structures (in typically different signatures) that was introduced by the second author as a link between the…
Universal minimal flows of extensions of and by compact groups
Dana Bartošová
Every topological group has up to isomorphism a unique minimal -flow that maps onto every minimal -flow, the universal minimal flow We show that if has a comp…
Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan
Dana Bartošová, Aleksandra Kwiatkowska
We generalize the finite version of Gowers' Ramsey theorem to multiple tetris-like operations and apply it to show that a group of homeomorphisms that preserve a "typical" linear o…
Lelek fan from a projective Fraisse limit
Dana Bartosova, Aleksandra Kwiatkowska
We show that a natural quotient of the projective Fraisse limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of t…
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
Dana Bartosova
In this paper, we compute universal minimal flows of groups of automorphisms of uncountable -homogeneous graphs, -free graphs, hypergraphs, partially ordered sets, and thei…