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Title page

Introduction

0.1. Why analyze Hod

0.2. A crash course on hod mice

0.3. The mouse set conjecture

0.4. The proof of MSC

0.5. The comparison theory of hod mice

0.6. Hod is a hod premouse

Chapter 1. Hod mice

1.1. Hybrid \J-structures

1.2. Some fine structure

1.3. Iteration trees and iteration strategies

1.4. Layered strategy premice

1.5. Iterations of Σ-mice

1.6. Hull condensation

1.7. Hod mice

Chapter 2. Comparison theory of hod mice

2.1. Hod pair constructions

2.2. Iterability of hod pair constructions

2.3. Universality of the fully backgrounded constructions

2.4. Coarse Γ-Woodin mice

2.5. Comparison under 𝐴𝐷⁺

2.6. Positional and commuting iteration strategies

2.7. The diamond comparison argument

Chapter 3. Hod mice revisited

3.1. The internal theory of hod premice

3.2. OD-full pointclasses

3.3. The derived models of hod mice

3.4. An anomaly

3.5. Getting branch condensation

3.6. Generic comparisons

3.7. Reorganizing hod mice

3.8. 𝑆-constructions

Chapter 4. Analysis of HOD

4.1. Suitability

4.2. 𝐵-iterability

4.3. The direct limit of iterates of hod mice

4.4. The computation of Hod

Chapter 5. Hod pair constructions

5.1. Stacking mice

5.2. Clause 4

5.3. Fullness preservation

5.4. The comparison argument revisited

5.5. Branch condensation

5.6. Γ(\P,Σ) when ł^{\P} is successor

5.7. 𝐵-iterability

5.8. Strongly ⃗𝐵-guided strategies

5.9. Summary

Chapter 6. A proof of the mouse set conjecture

6.1. The generation of the mouse full pointclasses

6.2. An analysis of stacks

6.3. Capturing of hod pairs

6.4. The mouse set conjecture

6.5. A last word

Appendix A. Descriptive set theory primer

A.1. Pointclasses

A.2. 𝐸𝑛𝑣(Γ)

A.3. 𝐴𝐷⁺

A.4. The derived model theorem

Bibliography

Index

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