13 papers
On Homomorphism Graphs
Sebastian Brandt, Yi-Jun Chang, Jan Grebík +3
We introduce a new type of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalizat…
Realizations of countable Borel equivalence relations
Joshua Frisch, Alexander Kechris, Forte Shinko +1
We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties.…
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.
Haar-positive closed subsets of Haar-positive analytic sets
Márton Elekes, Márk Poór, Zoltán Vidnyánszky
We show that every non-Haar-null analytic subset of contains a non-Haar-null closed subset. Moreover, we also prove that the codes of Haar-null analytic subsets, and…
On the existence of small antichains for definable quasi-orders
Raphaël Carroy, Benjamin D. Miller, Zoltán Vidnyánszky
We generalize Kada's definable strengthening of Dilworth's characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.
The structure of random automorphisms of the random graph
Udayan B. Darji, Márton Elekes, Kende Kalina +2
We give a complete description of the size of the conjugacy classes of the automorphism group of the random graph with respect to Christensen's Haar null ideal. It is shown that ev…