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On a cardinal invariant related to the Haar measure problem
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-02-12 , DOI: 10.1007/s11856-020-1975-2
Gianluca Paolini , Saharon Shelah

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

中文翻译:

关于与 Haar 测度问题相关的基数不变量

在[6]中,给定一个可度量的profinite群 G ,引入了连续统 $$\mathfrak{fm}$$fm ( G ) 的基数不变量,并在假设下给出了 G 的 Haar 测度问题的正解那个非( $$\mathcal{N}$$ N ) ≤ $$\mathfrak{fm}$$ fm ( G )。我们在此证明与 ZFC 一致的是存在可度量的超限群 G * 使得 non( $$\mathcal{N}$$ N ) > $$\mathfrak{fm}$$ fm ( G * ),因此证明 [6] 的策略不足以作为 Haar 度量问题的一般解决方案。
更新日期:2020-02-12
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