Antidiamond principles and topological applications

Eisworth, Todd; Nyikos, Peter

doi:10.1090/S0002-9947-09-04705-9

Antidiamond principles and topological applications
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Trans. Amer. Math. Soc. 361 (2009), 5695-5719 Request permission

Abstract:

We investigate some combinatorial statements that are strong enough to imply that $\diamondsuit$ fails (hence the name antidiamonds); yet most of them are also compatible with CH. We prove that these axioms have many consequences in set-theoretic topology, including the consistency, modulo large cardinals, of a Yes answer to a problem on linearly Lindelöf spaces posed by Arhangel’skiĭ and Buzyakova (1998).

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