A direct solution to the Generic Point Problem

Andy Zucker

A direct solution to the Generic Point Problem

Dynamical Systems 2017-08-01 v2 General Topology Logic

Authors: Andy Zucker

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.

Keywords

descriptive set theory

Cite

@article{arxiv.1705.00205,
  title  = {A direct solution to the Generic Point Problem},
  author = {Andy Zucker},
  journal= {arXiv preprint arXiv:1705.00205},
  year   = {2017}
}

Comments

This version extends the previous version by connecting the construction to the universal highly proximal extension

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