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Descriptive inner model theory

Published online by Cambridge University Press:  05 September 2014

Grigor Sargsyan
Grigor Sargsyan*
Affiliation:
Department of Mathematics, Rutgers University, Hill Center for the Mathematical Sciences, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA E-mail: grigor@math.rutgers.edu URL: http://math.rutgers.edu/~gs481
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Abstract

The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture (MSC). One particular motivation for resolving MSC is that it provides grounds for solving the inner model problem which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large.

Keywords

03E1503E4503E60Mouseinner model theorydescriptive set theoryhod mouse
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 19 , Issue 1 , March 2013 , pp. 1 - 55
Copyright
Copyright © Association for Symbolic Logic 2013

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