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 ${\mathrm{\Pi }}_1^1$ 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 ${\mathrm{\Pi }}_1^1$ sets are determined.

See also

• Projective determinacy

References

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