M. Zelený

activity

20132025

most citedOn Separable Determination of Sigma-P-Porous Sets in Banach Spaces

5 citations · 7 across the 7 of their papers we have counts for

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5 papers · 1 filter

math.LO2020

There is no bound on Borel classes of the graphs in the Luzin-Novikov theorem

P. Holicky, M. Zeleny

We show that for every ordinal $α \in [1, ω_{1})$ there is a closed set $F \subset 2^{ω} \times ω^{ω}$ such that for every $x \in 2^{ω}$ the section ${y \in ω^{ω}; (x, y) \in F}$ is a two-poin…

math.LO2018★ 2 cited

Analytic digraphs of uncountable Borel chromatic number under injective definable homomorphism

Dominique Lecomte, Miroslav Zeleny

We study the analytic digraphs of uncountable Borel chromatic number on Polish spaces, and compare them with the notion of injective Borel homomorphism. We provide some minimal dig…

math.LO2015

Universal and complete sets in martingale theory

Dominique Lecomte, Miroslav Zeleny

The Doob convergence theorem implies that the set of divergence of any martingale has measure zero. We prove that, conversely, any $G_δ σ$ subset of the Cantor space with Lebesgu…

math.LO2014

Borel chromatic number of closed graphs

Dominique Lecomte, Miroslav Zeleny

We construct, for each countable ordinal $ξ$ , a closed graph with Borel chromatic number two and Baire class $ξ$ chromatic number $ℵ_0$ .

math.LO2013

Descriptive complexity of countable unions of Borel rectangles

Dominique Lecomte, Miroslav Zeleny

We give, for each countable ordinal $ξ \geq 1$ , an example of a $Δ_{2}^{0}$ countable union of Borel rectangles that cannot be decomposed into countably many $Π_{ξ}^{0}$ rectangle…