The **proper forcing axiom** asserts that if P is proper and D_{α} is a dense subset of P for each α<ω_{1}, then there is a filter G P such that D_{α} ∩ G is nonempty for all α<ω_{1}.

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. If P is a countable support iteration of proper forcings, then P is proper. In general, proper forcings preserve .

Read more about Proper Forcing Axiom: Consequences, Consistency Strength, Other Forcing Axioms

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