Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees
Abstract
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, 65826586], it follows that (if there is a supercompact cardinal) every set of reals in L(R) is determined.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 September 1988
 DOI:
 10.1073/pnas.85.18.6587
 Bibcode:
 1988PNAS...85.6587W