# Algebra Seminar talk

2016-09-02

David **Schrittesser** (Københavns Universitet)*A Galvin-type Theorem for iterated Sacks forcing*

Abstract:

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.