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Homogeneously Suslin set

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In descriptive set theory, a set is said to be homogeneously Suslin if it is the projection of a homogeneous tree. is said to be -homogeneously Suslin if it is the projection of a -homogeneous tree.

If is a set and is a measurable cardinal, then is -homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinal implies that sets are determined.

See also

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References

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