Martin

Summary

Donald A. Martin

Martin's axiom for a cardinal κ states that for any partial order P satisfying the countable chain condition and any family D of dense sets in P of cardinality at most κ, there is a filter F on P such that $F \cap d$ is non-empty for every d in D

Martin's maximum states that if D is a collection of $\aleph_1$ dense subsets of a notion of forcing that preserves stationary subsets of ω₁, then there is a D-generic filter