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On a cardinal invariant related to the Haar measure problem

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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 non(\(\mathcal{N}\)) ≤ \(\mathfrak{fm}\)(G). We prove here that it is consistent with ZFC that there is a metrizable profinite group G* such that 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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Author information

Correspondence to Gianluca Paolini.

Additional information

Partially supported by European Research Council grant 338821. No. 1148 on Shelah’s publication list. The present paper was written while the first author was a post-doc research fellow at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem, supported by European Research Council grant 338821.

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Paolini, G., Shelah, S. On a cardinal invariant related to the Haar measure problem. Isr. J. Math. (2020). https://doi.org/10.1007/s11856-020-1975-2

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