Zobrazeno 1 - 10
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pro vyhledávání: '"Żeberski, Szymon"'
We work in the Cantor space $2^\omega$. The results of the paper adhere the following pattern. Let $\mathcal{I}\in \{\mathcal{M}, \mathcal{N}, \mathcal{M}\cap \mathcal{N}, \mathcal{E}\}$ and $T$ be a perfect, uniformly perfect or Silver tree. Then fo
Externí odkaz:
http://arxiv.org/abs/2405.13775
Autor:
Mazurkiewicz, Łukasz, Żeberski, Szymon
The aim of this paper is to give natural examples of $\mathbf{\Sigma}_1^1$-complete and $\mathbf{\Pi}_1^1$-complete sets. In the first part, we consider ideals on $\omega$. In particular, we show that the Hindman ideal $\mathcal{H}$ is $\mathbf{\Pi}_
Externí odkaz:
http://arxiv.org/abs/2310.07693
The motivation of this work are the two classical theorems on inscribing rectangles and squares into large subsets of the plane, namely Eggleston Theorem and Mycielski Theorem. Using Shoenfield Absoluteness Theorem we prove that for every Borel subse
Externí odkaz:
http://arxiv.org/abs/2307.07020
Autor:
Mazurkiewicz, Łukasz, Żeberski, Szymon
We study analytic and Borel subsets defined similarily to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e. division. It
Externí odkaz:
http://arxiv.org/abs/2305.11333
Autor:
Mazurkiewicz, Łukasz, Żeberski, Szymon
Publikováno v:
In Topology and its Applications 15 October 2024 356
A $\sigma$-ideal $\mathcal{I}$ on a Polish group $(X,+)$ has Smital Property if for every dense set $D$ and a Borel $\mathcal{I}$-positive set $B$ the algebraic sum $D+B$ is a complement of a set from $\mathcal{I}$. We consider several variants of th
Externí odkaz:
http://arxiv.org/abs/2102.03287
Using a game-theoretic approach we present a generalization of the classical result of Brzuchowski, Cicho\'n, Grzegorek and Ryll-Nardzewski on non-measurable unions. We also present applications of obtained results to Marczewski--Burstin representabl
Externí odkaz:
http://arxiv.org/abs/2011.11342
Two-dimensional version of the classical Mycielski theorem says that for every comeager or conull set $X\subseteq [0,1]^2$ there exists a perfect set $P\subseteq [0,1]$ such that $P\times P\subseteq X\cup \Delta$. We consider generalizations of this
Externí odkaz:
http://arxiv.org/abs/1905.09069
Publikováno v:
Bull. symb. log 26 (2020) 1-14
In this paper we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals $s_0$, $m_0$, $l_0$, and $cl_0$. We show that there exists a subset $A$ of the Baire space $\omega^\omega$ which is $s$-, $l$-, and $m$-n
Externí odkaz:
http://arxiv.org/abs/1712.05212
Publikováno v:
The Bulletin of Symbolic Logic, 2020 Mar 01. 26(1), 1-14.
Externí odkaz:
https://www.jstor.org/stable/26965199