On a Cardinal Invariant Related to the Haar Measure Problem

2018/09/27 by Paolini, Gianluca, Shelah, Saharon
#03E17 #20A15 #20E18 #22C05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1809.10442

Abstract

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

Related

• The Haar Measure Problem
• The Haar measure of a profinite n-ary group
• From Haar to Lebesgue via Domain Theory, Revised version
• Less than continuum many translates of a compact nullset may cover any infinite profinite group
• Formalized Haar Measure