Aleksander Cie'slak

collaborators

4 papers

math.LO2026

On Star operation and some ideals on the Baire space

Aleksander CieÅlak, Daria Perkowska, Szymon Å»eberski

We investigate several $I ¨ $ -ideals on the Baire space $I ¨ ^{I ¨} $ $(Z^{I ¨} )$ , introducing and studying the ideals $G$ and $SMZ^{+}$ , alongside the classical id…

math.LO2026

On antichain numbers and the splitting ideal

Aleksander CieÅlak

In this article, we study combinatorial properties of a certain ideal on $I ¨ $ , called the \emph{Splitting ideal}. We calculate its cardinal invariants and its position in the KatÄ…

math.LO2026

Cardinal invariants of idealized Miller null sets

Aleksander CieÅlak, Takehiko Gappo, Arturo MartÃnez-Celis +1

This paper provides an extensive study of the $I$ -Miller null ideals $M_{I}$ , $I ¨ $ -ideals on the Baire space parametrized by ideals $I$ on countable set…

math.LO2024

On ideals related to Laver and Miller trees

Aleksander CieÅlak, Arturo MartÃnez-Celis

In this work we consider the ideals $m^{0} (I)$ and $ℓ^{0} (I)$ , ideals generated by the $I$ -positive Miller trees and $I$ -positive Laver trees…