ANTIDIAMOND PRINCIPLES AND TOPOLOGICAL APPLICATIONS

We investigate some combinatorial statements that are strong enough to imply that lozenge 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, mdoulo large cardinals, of a Yes answer to a problem oil linearly Lindelof spaces posed by Arhangel'skii and Buzyakova (1998).