Mouse Sets

Details Mouse Sets Mouse Sets

1996-06-18

arxiv.org/abs/math/9606207v1

Mathematics

Logic

Scientific paper

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.

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