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arXiv · 2510.27435

An Ideal Zoo in the Baire Space

Łukasz Mazurkiewicz·Marcin Michalski·Szymon Żeberski
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Abstract

In this paper, we study the translations into the Baire space of several well-known $\sigma$-ideals and families originally defined on the Cantor space, using their combinatorial characterizations. These include the ideals of null sets, small sets, those generated by closed measure-zero sets, and the meager sets, leading to their "fake" analogues in the Baire space. We also parametrize families related to null sets by functions from $\omega^\omega$. Several structural properties and relations between these families are investigated, including whether they form ideals, the existence of large chains and antichains, orthogonality, the $\kappa$-chain condition, and the determination of certain cardinal invariants.

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Łukasz Mazurkiewicz, Marcin Michalski, Szymon Żeberski. 2025-10-31. An Ideal Zoo in the Baire Space. https://arxiv.org/abs/2510.27435

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