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A friendly iteration forcing that the four cardinal characteristics of $\mathcal E$ can be pairwise different

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Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated… Click to show full abstract

Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\ additivity, covering, uniformity and cofinality) are pairwise different.

Keywords: friendly iteration; cardinal characteristics; pairwise different; iteration forcing

Journal Title: Colloquium Mathematicum
Year Published: 2022

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