Splitting positive sets. (English) Zbl 07761595
Summary: We introduce a class of cardinal invariants \(\mathfrak{s}_{\mathcal{I}}\) for ideals \(\mathcal{I}\) on \(\omega\) which arise naturally from the FinBW property introduced by Filipów et al. (2007). Let \(\mathcal{I}\) be an ideal on \(\omega\). Define
\[
\mathfrak{s}_{\mathcal{I}} = \min \{ |X|:X \subset [\omega ]^{\omega},\forall B \in\mathcal{I}^+,\,\exists x \in X(B\backslash x,B \cap x \in [\omega]^{\omega})\}.
\]
We characterize them and compare them with other cardinal invariants of the continuum.
MSC:
| 03E17 | Cardinal characteristics of the continuum |
| 03E15 | Descriptive set theory |
| 40A30 | Convergence and divergence of series and sequences of functions |
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