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, 6582-6586], it follows that (if there is a supercompact cardinal) every set of reals in L(R) is determined.
Keywords: set theory, descriptive set theory, large cardinals
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Selected References
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- Martin D. A., Steel J. R. Projective determinacy. Proc Natl Acad Sci U S A. 1988 Sep;85(18):6582–6586. doi: 10.1073/pnas.85.18.6582. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Martin D. A., Steel J. R. Projective determinacy. Proc Natl Acad Sci U S A. 1988 Sep;85(18):6582–6586. doi: 10.1073/pnas.85.18.6582. [DOI] [PMC free article] [PubMed] [Google Scholar]