PlanetMath: Martin's axiom

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Martin's axiom

(Definition)

For any cardinal $\kappa$ , Martin's Axiom for $\kappa$ ( $MA_\kappa$ ) states that if is a partial order satisfying ccc then given any set of $\kappa$ dense subsets of , there is a directed subset intersecting each such subset. Martin's Axiom states that $MA_\kappa$ holds for every $\kappa<2^{\aleph_0}$ .

"Martin's axiom" is owned by Henry.

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Also defines:

Attachments:: Martin's axiom and the continuum hypothesis (Result) by Henry
Martin's axiom is consistent (Result) by mathcam

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Cross-references: subsets, ccc, partial order, states, cardinal
There are 9 references to this entry.

This is version 3 of Martin's axiom, born on 2002-08-04, modified 2003-02-04.
Object id is 3266, canonical name is MartinsAxiom.
Accessed 4362 times total.

Classification:

AMS MSC:

03E50 (Mathematical logic and foundations :: Set theory :: Continuum hypothesis and Martin's axiom)

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