---
tag: 45RYSEAN2P
kind: concept
name: Martin
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section M
    note: adopted
    mention: wikipedia://en/43580500#VOES
    sections: [Summary]
inventory: [PDZK6Y73PC]
---

## 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 ω<sub>1</sub>, then there is a *D*-generic filter