Bulletin of Symbolic Logic 19 (1):1-55 (2013)

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. 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 Mouse   inner model theory   descriptive set theory   hod mouse
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DOI 10.2178/bsl.1901010
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References found in this work BETA

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Citations of this work BETA

Axiom I 0 and Higher Degree Theory.Xianghui Shi - 2015 - Journal of Symbolic Logic 80 (3):970-1021.
Realizing an AD+ Model as a Derived Model of a Premouse.Yizheng Zhu - 2015 - Annals of Pure and Applied Logic 166 (12):1275-1364.
Hod Up to ADR+Θ is Measurable.Rachid Atmai & Grigor Sargsyan - 2019 - Annals of Pure and Applied Logic 170 (1):95-108.

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