The proper forcing axiom asserts that if P is proper and Dα is a dense subset of P for each α<ω1, then there is a filter G P such that Dα ∩ G is nonempty for all α<ω1.
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 .
Other articles related to "proper forcing axiom, forcing axiom, forcing axioms, axioms":
... The bounded proper forcing axiom (BPFA) is a weaker variant of PFA which instead of arbitrary dense subsets applies only to maximal antichains of size ω1 ... Martin's maximum is the strongest possible version of a forcing axiom ... Forcing axioms are viable candidates for extending the axioms of set theory as an alternative to large cardinal axioms ...
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