 The proper forcing axiom asserts that if P is proper and Dα is a dense subset of P for each α1, then there is a filter G formula_3 P such that Dα ∩ G is nonempty for all α1.The class of proper forcings, to which PFA can be applied, is rather large.For example, standard arguments show that if P is ccc or ω-closed, then P is proper.