Supercompact cardinals, sets of reals, and weakly homogeneous trees. (English) Zbl 0656.03037

It is shown that if there exists a supercompact cardinal then every set of reals which is an element of L(\({\mathbb{R}})\) is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of D. A. Martin and J. R. Steel [reviewed above (see Zbl 0656.03036)], it follows that (if there is a supercompact cardinal) every set of reals in L(\({\mathbb{R}})\) is determined.


03E60 Determinacy principles
03E55 Large cardinals
03E15 Descriptive set theory


Zbl 0656.03036
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