Jan Grebík

activity

20162021

collaborators

Showing math.LOShow all

5 papers · 1 filter

math.LO2021

Approximate Schreier decorations and approximate Kőnig's line coloring Theorem

Jan Grebik

Following recent result of L. M. T\' oth [arXiv:1906.03137] we show that every $2Δ$ -regular Borel graph $G$ with a (not necessarily invariant) Borel probability measure a…

math.LO2020

$σ$ -Lacunary actions of Polish groups

Jan Grebik

We show that every essentially countable orbit equivalence relation induced by a continuous action of a Polish group on a Polish space is $σ$ -lacunary. In combination with [Invent.…

math.LO2017

Borel selector for hypergraphons

Jan Grebik

We show that there is a Borel way of choosing a representative of a $k$ -uniform hypergraphon. This extends the result of Orbanz and Szegedy where this was shown for graphons.

math.LO2017

Bases and selectors for tall families

Jan Grebik, Carlos Uzcategui

We show that the Nash-Williams theorem has a uniform version and that the Galvin theorem does not. We show that there is an $F_{σ}$ tall ideal on $N$ without a Borel selecto…

math.LO2016

An example of a Fraïssé class without a Katětov functor

Jan Grebík

We disprove a conjecture from [W. Kubiś, D. Mašulović, Katětov functors, preprint, http://arxiv.org/abs/1412.1850] by showing the existence of a Fraïssé class $C$ which d…

Approximate Schreier decorations and approximate Kőnig's line coloring Theorem

σ-Lacunary actions of Polish groups

Borel selector for hypergraphons

Bases and selectors for tall families

An example of a Fraïssé class without a Katětov functor

$σ$ -Lacunary actions of Polish groups