Algebra Seminar talk
David Schrittesser (Københavns Universitet)
A Galvin-type Theorem for iterated Sacks forcing
Galvin's theorem says that for every sufficiently nice coloring of pairs of reals, there is a perfect homogeneous set. It can be used to show interesting statements in the Sacks extension: such as, by recent joint work with Tönquist, that there is an effectively co-analytic maximal orthogonal family of measures.
In this talk I shall sketch a proof that a theorem analogous to Galvin's Theorem holds for iterated Sacks forcing. This can be used similarly to show the above (among other results) in a model where the continuum hypothesis fails.