Английская Википедия:Homogeneously Suslin set
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In descriptive set theory, a set <math>S</math> is said to be homogeneously Suslin if it is the projection of a homogeneous tree. <math>S</math> is said to be <math>\kappa</math>-homogeneously Suslin if it is the projection of a <math>\kappa</math>-homogeneous tree.
If <math>A\subseteq{}^\omega\omega</math> is a <math>\mathbf{\Pi}_1^1</math> set and <math>\kappa</math> is a measurable cardinal, then <math>A</math> is <math>\kappa</math>-homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinal implies that <math>\mathbf{\Pi}_1^1</math> sets are determined.
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