Descriptive inner model theory

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 area...

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Bibliographic Details
Published in:The bulletin of symbolic logic 2013-03, Vol.19 (1), p.1-55
Main Author: Sargsyan, Grigor
Format: Article
Language:English
Subjects:
03E15
03E45
03E60
Axioms
Condensation
descriptive set theory
Determinacy
hod mouse
inner model theory
Large cardinal properties
Mathematical logic
Mathematical set theory
Mathematics
Model theory
Mouse
Multilevel models
Steels
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Summary: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.
ISSN:1079-8986
1943-5894
DOI:10.2178/bsl.1901010