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2 results

  • Chapter 1 - Introduction

  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book:
    The Largest Suslin Axiom
    Published online:
    07 June 2024
    Print publication:
    27 June 2024, pp 1-8

  • Summary

    This chapter introduces the main concepts and the problems to be investigated by the book. In particular, the chapter defines the Largest Suslin Axiom (LSA) and the minimal model of LSA. The chapter summarizes the main theorems to be proved in the book: HOD of the minimal model of LSA satisfies the Generalized Continuum Hypothesis, the Mouse Set Conjecture holds in the minimal model of LSA, the consistency of LSA from large cardinals, the consistency of LSA from strong forcing axioms like PFA.

The Largest Suslin Axiom
  • Grigor Sargsyan, Nam Trang
  • Published online:
    07 June 2024
    Print publication:
    27 June 2024
  • 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.