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A direct solution to the Generic Point Problem (1705.00205v2)
Published 29 Apr 2017 in math.DS, math.GN, and math.LO
Abstract: We provide a new proof of a recent theorem of Ben-Yaacov, Melleray, and Tsankov. If $G$ is a Polish group and $X$ is a minimal, metrizable $G$-flow with all orbits meager, then the universal minimal flow $M(G)$ is non-metrizable. In particular, we show that given $X$ as above, the universal highly proximal extension of $X$ is non-metrizable.
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