Ideal independent families and the ultrafilter number

Journal of Symbolic Logic 86 (1):128-136 (2021)
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Abstract

We say that $\mathcal {I}$ is an ideal independent family if no element of ${\mathcal {I}}$ is a subset mod finite of a union of finitely many other elements of ${\mathcal {I}}.$ We will show that the minimum size of a maximal ideal independent family is consistently bigger than both $\mathfrak {d}$ and $\mathfrak {u},$ this answers a question of Donald Monk.

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Con(U>I).Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (6):433-443.

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