Your browser version may not work well with NCBI's Web applications. More information here...
1: Proc Natl Acad Sci U S A. 1988 Sep;85(18):6587-6591.Click here to read Links

Supercompact cardinals, sets of reals, and weakly homogeneous trees.

Woodin WH.

Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125.

It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 6582-6586], it follows that (if there is a supercompact cardinal) every set of reals in L(R) is determined.

PMID: 16593979 [PubMed - as supplied by publisher]

PMCID: PMC282022