5 papers · 1 filter
Ramsey, expanders, and Borel chromatic numbers
Jan Grebík, Zoltán Vidnyánszky
We construct bounded degree acyclic Borel graphs with large Borel chromatic number using a graph arising from Ramsey theory and limits of expander sequences.
Borel equivalence relations induced by actions of tsi Polish groups
Jan Grebík
We study Borel equivalence relations induced by Borel actions of tsi Polish groups on standard Borel spaces. We characterize when such an equivalence relation admits classification…
Tall subideals of tall analytic ideals
Jan Grebík, Zoltán Vidnyánszky
Answering a question of Hrušák, we show that every analytic tall ideal on contains an tall ideal. We also give an example of an tall ideal without a Borel selector.
Scrambled Cantor sets
Stefan Geschke, Jan Grebík, Benjamin D. Miller
We show that Li-Yorke chaos ensures the existence of a scrambled Cantor set.
No minimal tall Borel ideal in the Katětov order
Jan Grebík, Michael Hrušák
Answering a question of the second listed author we show that there is no tall Borel ideal minimal among all tall Borel ideals in the Katětov order.