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 11 - A proof of square in LSA-small HOD mice
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 presents a proof $\square_{\kappa,2}$ holds in a lsa-small hod mouse $\mathcal{P}$ for all cardinals $\kappa$ of $\mathcal{P}$. The proof adapts a well-known construction of $\square$ in extender models by Schimmerling-Zeman. The main challenge to overcome in this situation is that the full condensation lemma, which holds for extender models, does not hold in hod mice. The main application of this result is in the proof of consistency of LSA in Chapter 12.
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- The Largest Suslin Axiom , pp. 309 - 334Publisher: Cambridge University PressPrint publication year: 2024