The Largest Suslin Axiom

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.

• Provides the first proof of the consistency of the Largest Suslin Axiom relative to large cardinals
• Develops the core model induction, a universal technique for building models of determinacy axioms, up to the region of the Largest Suslin Axiom
• Proves the Mouse Set Conjecture, one of the central conjectures of descriptive inner model theory