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.

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