Book contents
- Frontmatter
- Dedication
- Contents
- Chapter 1 Introduction
- Chapter 2 Hybrid 𝒥-structures
- Chapter 3 Short tree strategy mice
- Chapter 4 A comparison theory of HOD mice
- Chapter 5 HOD mice revisited
- Chapter 6 The internal theory of LSA HOD mice
- Chapter 7 Analysis of HOD
- Chapter 8 Models of LSA as derived models
- Chapter 9 Condensing sets
- Chapter 10 Applications
- Chapter 11 A proof of square in LSA-small HOD mice
- Chapter 12 LSA from PFA
- References
- Index
Chapter 10 - Applications
Published online by Cambridge University Press: 07 June 2024
- Frontmatter
- Dedication
- Contents
- Chapter 1 Introduction
- Chapter 2 Hybrid 𝒥-structures
- Chapter 3 Short tree strategy mice
- Chapter 4 A comparison theory of HOD mice
- Chapter 5 HOD mice revisited
- Chapter 6 The internal theory of LSA HOD mice
- Chapter 7 Analysis of HOD
- Chapter 8 Models of LSA as derived models
- Chapter 9 Condensing sets
- Chapter 10 Applications
- Chapter 11 A proof of square in LSA-small HOD mice
- Chapter 12 LSA from PFA
- References
- Index
Summary
This chapter gives various applications of the theory developed in the previous chapters. The first application is a proof of generation of mouse full pointclasses assuming Strong Mouse Capturing. The second application is a proof that Strong Mouse Capturing holds in the minimal model of LSA; so the Mouse Set Conjecture is true in all models of AD^+ up to the minimal model of LSA. The third application is a proof of consistency of LSA from the existence of a Woodin limit of Woodin cardinals.
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- Chapter
- Information
- The Largest Suslin Axiom , pp. 273 - 308Publisher: Cambridge University PressPrint publication year: 2024