The existence of a connected meager in itself 𝖢𝖣𝖧 space is independent of 𝖹𝖥𝖢

Hrušák, Michael; van Mill, Jan

doi:10.1090/proc/13434

The existence of a connected meager in itself $\mathsf {CDH}$ space is independent of $\mathsf {ZFC}$
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Proc. Amer. Math. Soc. 146 (2018), 2689-2695 Request permission

Abstract:

We show that the existence of a countable dense homogeneous metric space which is connected and meager in itself is independent of $\mathsf {ZFC}$.

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