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

preprint2022arXivOpen access

Abstract

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

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