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Published September 15, 1988 | Published
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Supercompact cardinals, sets of reals, and weakly homogeneous trees

Woodin, W. Hugh
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Abstract

It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of [Note: See the image of page 6587 for this formatted text] 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 [Note: See the image of page 6587 for this formatted text] L(R) is determined.

Additional Information

© 1988 by the National Academy of Sciences. Communicated by Robert M. Solovay, May 12, 1988 (received for review November 7, 1987). This research was partially supported by National Science Foundation Grant DMS 8416349. W.H.W. is an A.P. Sloan Foundation Fellow. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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