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arXiv · 1906.06608

Cicho\'n's maximum without large cardinals

Martin Goldstern·Jakob Kellner·Diego A. Mejía·Saharon Shelah
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Abstract

Cicho\'n's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent that all entries of Cicho\'n's diagram are pairwise different (apart from $\textrm{add}(\mathcal{M})$ and $\textrm{cof}(\mathcal{M})$, which are provably equal to other entries). However, the consistency proofs so far required large cardinal assumptions. In this work, we show the consistency without such assumptions.

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Martin Goldstern, Jakob Kellner, Diego A. Mejía, Saharon Shelah. 2019-06-15. Cicho\'n's maximum without large cardinals. https://arxiv.org/abs/1906.06608

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