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math.LO2023
Ideal Analytic sets
Łukasz Mazurkiewicz, Szymon Żeberski
The aim of this paper is to give natural examples of -complete and -complete sets. In the first part, we consider ideals on . In particular, we show…
math.LO2023
Around Eggleston Theorem
Marcin Michalski, Robert Rałowski, Szymon Żeberski
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. Usi…
math.GN2023
Sequences with increasing subsequence
Łukasz Mazurkiewicz, Szymon Żeberski
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…