Sacks forcing and the total failure of Martin's axiom (Q1066892)

In topological language Martin's axiom asserts that no compact ccc space is the union of less than \(2^{\omega_ 0}\) closed nowhere dense sets. The author shows that Martin's axiom can fail totally: using side-by-side Sacks forcing he shows that \(2^{\omega_ 0}\) can be big and yet every compact ccc space without isolated points is the union of \(\omega_ 1\) closed nowhere dense sets. The paper also contains a good introduction to side-by-side Sacks forcing.