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Hod mice and the Mouse Set Conjecture

About this Title

Grigor Sargsyan

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)
Published electronically: November 6, 2014
Keywords:Mouse, inner model theory, descriptive set theory

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Table of Contents


  • Introduction
  • Chapter 1. Hod mice
  • Chapter 2. Comparison theory of hod mice
  • Chapter 3. Hod mice revisited
  • Chapter 4. Analysis of HOD
  • Chapter 5. Hod pair constructions
  • Chapter 6. A proof of the mouse set conjecture
  • Appendix A. Descriptive set theory primer


We develop the theory of hod mice below is regular". We use this theory to show that of the minimal model of is regular" satisfies . Moreover, we show that the Mouse Set Conjecture is true in the minimal model of is regular”.

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