Abstract
Publisher Summary This chapter presents various theorems to generalize when one should expect Martin's axiom (MA) to be useful. Some of the theorems discussed in the chapter are if ZFC (Zermelo–Fraenkel set theory with the axiom of choice) is consistent, ZFC + MA + ¬ continuum hypothesis (CH) is consistent; if X is a ccc compact Hausdorff space, X is not the union of less than 2 ω nowhere dense sets; there is no Souslin tree; the product of any family of ccc spaces is ccc; and every Aronszajn tree is the union of countably many antichains. In topology MA + ¬ CH can be used to construct a variety of normal but not collectionwise normal spaces. MA can be used to deny the existence of certain pathologies in countable antichain condition (ccc) spaces.
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