Homogeneously Suslin set
# 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 $\kappa$-homogeneously Suslin if it is the projection of a $\kappa$-homogeneous tree.

If $A\subseteq^{\omega }\omega$ is a $\mathbf {\Pi } _{1}^{1}$ set and $\kappa$ is a measurable cardinal, then $A$ is $\kappa$-homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinal implies that $\mathbf {\Pi } _{1}^{1}$ sets are determined.

