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Hod mice and the Mouse Set Conjecture
About this Title
Grigor Sargsyan, Department of Mathematics, Rutgers University, 100 Frelinghuysen Road, Piscataway, New Jersey 08854
Publication: Memoirs of the American Mathematical Society
Publication Year:
2015; Volume 236, Number 1111
ISBNs: 978-1-4704-1692-8 (print); 978-1-4704-2277-6 (online)
DOI: https://doi.org/10.1090/memo/1111
Published electronically: November 6, 2014
Keywords: Mouse,
inner model theory,
descriptive set theory,
hod mouse
MSC: Primary 03E15, 03E45, 03E60
Table of Contents
Chapters
- Introduction
- 1. Hod mice
- 2. Comparison theory of hod mice
- 3. Hod mice revisited
- 4. Analysis of HOD
- 5. Hod pair constructions
- 6. A proof of the mouse set conjecture
- A. Descriptive set theory primer
Abstract
We develop the theory of hod mice below $AD_{\mathbb {R}}+“\Theta$ is regular". We use this theory to show that $\textrm {{HOD}}$ of the minimal model of $AD_{\mathbb {R}}+“\Theta$ is regular" satisfies $GCH$. Moreover, we show that the Mouse Set Conjecture is true in the minimal model of $AD_{\mathbb {R}}+“\Theta$ is regular”.- Howard S. Becker and Alexander S. Kechris, Sets of ordinals constructible from trees and the third Victoria Delfino problem, Axiomatic set theory (Boulder, Colo., 1983) Contemp. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1984, pp. 13–29. MR 763889, DOI 10.1090/conm/031/763889
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