Homogeneously Suslin set

In descriptive set theory, a set S is said to be homogeneously Suslin if it is the projection of a homogeneous tree. S is said to be κ -homogeneously Suslin if it is the projection of a κ -homogeneous tree.

If A ⊆ ω ω is a Π 1 1 set and κ is a measurable cardinal, then A is κ -homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinal implies that Π 1 1 sets are determined.