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Chapter 12 - LSA from PFA

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 presents a construction of the minimal model of LSA from a hypothesis implied by strong forcing axioms such as PFA and by large cardinal hypotheses such as the existence of a strongly compact cardinal. Consequently, LSA is consistent relative to PFA and LSA is consistent relative to the existence of a strongly compact cardinal. This chapter is an application of the theory developed in the previous chapters and the core model induction technique, which is a general method for calibrating consistency strength of strong theories.

Keywords

Condensing setcore model inductionPFALSAsuitable hod premousevalidated iterationcorrectly backgrounded extenderX-validated sts constructionhybrid$ K^c$-construction
Type
Chapter
Information
The Largest Suslin Axiom , pp. 335 - 384
Publisher: Cambridge University Press
Print publication year: 2024

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  • LSA from PFA
  • 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/10.1017/9781009520683.012
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  • LSA from PFA
  • 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/10.1017/9781009520683.012
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.

  • LSA from PFA
  • 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/10.1017/9781009520683.012
Available formats
×