1996/06/18 by Mitch Rudominer, Rudominer, Mitch
Biochemistry, Genetics and Molecular Biology · Mathematics · #Cell Image Analysis Techniques #FOS: Mathematics #Gene expression and cancer classification #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.math/9606207
arxiv created 1996/06/18 · openalex publication_date 1996/06/18 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this paper we explore a connection between descriptive set theory and inner model theory. From descriptive set theory, we will take a countable, definable set of reals, A. We will then show that A is equal to the reals of M, where M is a canonical model from inner model theory. In technical terms, M is a ''mouse''. Consequently, we say that A is a mouse set. For a concrete example of the type of set A we are working with, let OD(n) be the set of reals which are Sigma-n definable over the omega-first level of the model L(R), from an ordinal parameter. In this paper we will show that for all n, OD(n) is a mouse set. Our work extends some similar results due to D.A. Martin, J.R. Steel, and H. Woodin. Several interesting questions in this area remain open.