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 $Asubseteq\{\}^omegaomega$ 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.

ee also

* Projective determinacy

References

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