The Largest Suslin Axiom

A thorough study of the minimal model of the Largest Suslin Axiom, including the first proof of its consistency.

Grigor Sargsyan (Author), Nam Trang (Author)

9781009520713, Cambridge University Press

Hardback, published 27 June 2024

404 pages
22.9 x 15.2 x 2.7 cm, 0.692 kg

Developing the theory up to the current state-of-the art, this book studies the minimal model of the Largest Suslin Axiom (LSA), which is one of the most important determinacy axioms and features prominently in Hugh Woodin's foundational framework known as the Ultimate L. The authors establish the consistency of LSA relative to large cardinals and develop methods for building models of LSA from other foundational frameworks such as Forcing Axioms. The book significantly advances the Core Model Induction method, which is the most successful method for building canonical inner models from various hypotheses. Also featured is a proof of the Mouse Set Conjecture in the minimal model of the LSA. It will be indispensable for graduate students as well as researchers in mathematics and philosophy of mathematics who are interested in set theory and in particular, in descriptive inner model theory.

1. Introduction
2. Hybrid J-structures
3. Short tree strategy mice
4. A comparison theory of HOD mice
5. HOD mice revisited
6. The internal theory of LSA HOD mice
7. Analysis of HOD
8. Models of LSA as derived models
9. Condensing sets
10. Applications
11. A proof of square in LSA-small HOD mice
12. LSA from PFA
References
Index.

Subject Areas: Mathematical foundations [PBC]