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Chapter 12 - LSA from PFA

Published online by Cambridge University Press:  aN Invalid Date NaN

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
  • 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
  • Chapter DOI: https://doi.org/10.1017/9781009520683.012
Available formats
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  • LSA from PFA
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Chapter DOI: https://doi.org/10.1017/9781009520683.012
Available formats
×