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Chapter 1 - Introduction

Published online by Cambridge University Press:  07 June 2024

Grigor Sargsyan  and
Nam Trang
Grigor Sargsyan
Affiliation:
Polish Academy of Sciences
Nam Trang
Affiliation:
University of North Texas
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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.

Keywords

Mouseinner model theorydescriptive set theoryhod mousedeterminacylarge cardinalsthe Largest Suslin AxiomHODProper Forcing Axiomthe core model induction
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Chapter
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The Largest Suslin Axiom , pp. 1 - 8
Publisher: Cambridge University Press
Print publication year: 2024

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  • Introduction
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Online publication: 07 June 2024
  • Chapter DOI: https://doi.org/10.1017/9781009520683.001
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Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Introduction
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Online publication: 07 June 2024
  • Chapter DOI: https://doi.org/10.1017/9781009520683.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Online publication: 07 June 2024
  • Chapter DOI: https://doi.org/10.1017/9781009520683.001
Available formats
×