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arXiv · 1809.10442

On a Cardinal Invariant Related to the Haar Measure Problem

Gianluca Paolini·Saharon Shelah
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Abstract

In [6], given a metrizable profinite group $G$, a cardinal invariant of the continuum $\mathfrak{fm}(G)$ was introduced, and a positive solution to the Haar Measure Problem for $G$ was given under the assumption that $\mathrm{non}(\mathcal{N}) \leq \mathfrak{fm}(G)$. We prove here that it is consistent with ZFC that there is a metrizable profinite group $G_*$ such that $\mathrm{non}(\mathcal{N}) > \mathfrak{fm}(G_*)$, thus demonstrating that the strategy of [6] does not suffice for a general solution to the Haar Measure Problem.

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Gianluca Paolini, Saharon Shelah. 2018-09-27. On a Cardinal Invariant Related to the Haar Measure Problem. https://arxiv.org/abs/1809.10442

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