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Article overview
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Non-meager free sets and independent families | Andrea Medini
; Dušan Repovš
; Lyubomyr Zdomskyy
; | Date: |
1 Aug 2015 | Abstract: | Our main result is that, given a collection $mathcal{R}$ of meager relations
on a Polish space $X$ such that $|mathcal{R}|leqomega$, there exists a dense
Baire subspace $F$ of $X$ (equivalently, a nowhere meager subset of $X$) such
that $F$ is $R$-free for every $Rinmathcal{R}$. This generalizes a recent
result of Banakh and Zdomskyy. Furthermore, assuming Martin’s Axiom for
countable posets, our result can be strengthened by substituting
"$|mathcal{R}|leqomega$" with "$|mathcal{R}|<mathfrak{c}$" and "Baire"
with "completely Baire". As an application, we show that there exists a
non-meager independent family on $omega$, and define the corresponding
cardinal invariant. | Source: | arXiv, 1508.0124 | Services: | Forum | Review | PDF | Favorites |
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