Homogeneously Suslin set explained

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 \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 \Pi ^{1} _{1} sets are determined.

See also

• Projective determinacy

References

• Martin, Donald A. and John R. Steel. Jan 1989. A Proof of Projective Determinacy. Journal of the American Mathematical Society. 2. 1. 71–125. 10.2307/1990913. American Mathematical Society. 1990913. free.