A new small Dowker space

Assaf Rinot; Roy Shalev; Stevo Todorcevic

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arXiv · 2209.10504

A new small Dowker space

Assaf Rinot·Roy Shalev·Stevo Todorcevic

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Abstract

It is proved that if there exists a Luzin set, or if either the stick principle or diamond(b) hold, then a strong instance of the guessing principle $\clubsuit_{AD}$ holds at the first uncountable cardinal. In particular, any of the above hypotheses entails the existence of a Dowker space of size $\aleph_1$.

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Assaf Rinot, Roy Shalev, Stevo Todorcevic. 2022-09-21. A new small Dowker space. https://arxiv.org/abs/2209.10504

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