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Chapter 9 - Condensing sets

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 develops the theory of condensing sets. Condensing sets give rise to iteration strategies with nice condensation properties. We show the existence of condensing sets under various hypotheses: AD^+ and PFA. We will use the existence of condensing sets in AD^+ in the proof of generation of pointclasses in Chapter 10. We will use the existence of condensing sets in Chapter 12 to construct a model of LSA under PFA.

Keywords

Condensing setstrongly condensing sethonest extensionmouse full pointclass
Type
Chapter
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The Largest Suslin Axiom , pp. 235 - 272
Publisher: Cambridge University Press
Print publication year: 2024

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  • Condensing sets
  • 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/10.1017/9781009520683.009
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  • Condensing sets
  • 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/10.1017/9781009520683.009
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.

  • Condensing sets
  • 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/10.1017/9781009520683.009
Available formats
×