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 ${\displaystyle A\subseteq {}^{\omega }\omega }$ is a ${\displaystyle \mathbf {\Pi } _{1}^{1}}$ 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 ${\displaystyle \mathbf {\Pi } _{1}^{1}}$ 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. American Mathematical Society. 2 (1): 71–125. doi:10.2307/1990913. JSTOR 1990913.