Supersaturated ideals

Ashutosh Kumar; Dilip Raghavan

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arXiv · 2106.15663

Supersaturated ideals

Ashutosh Kumar·Dilip Raghavan

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Abstract

A $\sigma$-ideal $\cal{I}$ on a set $X$ is supersaturated if for every family $\cal{F}$ of $\cal{I}$-positive sets with $|\cal{F}| < \mathrm{add}(\cal{I})$, there exists a countable set that meets every set in $\cal{F}$. We show that many well-known ccc forcings preserve supersaturation. We also show that the existence of supersaturated ideals is independent of ZFC plus "There exists an $\omega_1$-saturated $\sigma$-ideal".

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BibTeX RIS

Ashutosh Kumar, Dilip Raghavan. 2021-06-29. Supersaturated ideals. https://arxiv.org/abs/2106.15663

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