Antidiamond principles and topological applications

Abstract

We investigate some combinatorial statements that are strong enough to imply that ♦ 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'ski˘ ı and Buzyakova (1998).