6 citations · 15 across the 10 of their papers we have counts for
17 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…
The structure of random automorphisms of the rational numbers
Udayan B. Darji, Márton Elekes, Kende Kalina +2
In order to understand the structure of the "typical" element of an automorphism group, one has to study how large the conjugacy classes of the group are. For the case when typical…
A Haar meager set that is not strongly Haar meager
Márton Elekes, Donát Nagy, Márk Poór +1
Following Darji, we say that a Borel subset of an abelian Polish group is Haar meager if there is a compact metric space and a continuous function such th…
Embeddability on functions: order and chaos
Raphaël Carroy, Yann Pequignot, Zoltán Vidnyánszky
We study the quasi-order of topological embeddability on definable functions between Polish zero-dimensional spaces. We first study the descriptive complexity of this quasi-order r…
Infinite monochromatic sumsets for colourings of the reals
Péter Komjáth, Imre Leader, Paul A. Russell +3
N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of so that no infinite sumset is monochromatic…
A complexity problem for Borel graphs
Stevo Todorčević, Zoltán Vidnyánszky
We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift…
The structure of random automorphisms of countable structures
Udayan B. Darji, Márton Elekes, Kende Kalina +2
In order to understand the structure of the `typical' element of an automorphism group, one has to study how large the conjugacy classes of the group are. When typical is meant in…
The structure of random homeomorphisms
Udayan B. Darji, Márton Elekes, Kende Kalina +2
In order to understand the structure of the "typical" element of a homeomorphism group, one has to study how large the conjugacy classes of the group are. When typical means generi…
Almost disjoint refinements and mixing reals
Barnabás Farkas, Yurii Khomskii, Zoltán Vidnyánszky
We investigate families of subsets of with almost disjoint refinements in the classical case as well as with respect to given ideals on . More precisely, we study the follow…
Naively Haar null sets in Polish groups
Márton Elekes, Zoltán Vidnyánszky
Let be a Polish group. We say that a set is Haar null if there exists a universally measurable set and a Borel probability measure such…
Characterization of order types of pointwise linearly ordered families of Baire class 1 functions
Márton Elekes, Zoltán Vidnyánszky
In the 1970s M. Laczkovich posed the following problem: Let denote the set of Baire class functions defined on an uncountable Polish space equipped with…
Ranks on the Baire class functions
Márton Elekes, Viktor Kiss, Zoltán Vidnyánszky
In 1990 Kechris and Louveau developed the theory of three very natural ranks on the Baire class functions. A rank is a function assigning countable ordinals to certain objects,…