On Countable Stationary Towers

Yo Matsubara*, Toshimichi Usuba

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate properties of countable stationary towers. We derive the regularity properties of sets of reals in L(R) from some properties of countable stationary towers without explicit use of strong large cardinals such as Woodin cardinals. We also introduce the notion of semiprecipitousness and investigate its relation to precipitousness and presaturation of countable stationary towers. We show that precipitousness of countable stationary towers of weakly compact height implies the regularity properties of sets of reals in L(R).

Original languageEnglish
Title of host publicationAdvances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions
EditorsToshiyasu Arai, Makoto Kikuchi, Satoru Kuroda, Mitsuhiro Okada, Teruyuki Yorioka
PublisherSpringer
Pages133-141
Number of pages9
ISBN (Print)9789811641725
DOIs
Publication statusPublished - 2021
EventSymposium on Advances in Mathematical Logic, SAML 2018 - Kobe, Japan
Duration: 2018 Sep 182018 Sep 20

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume369
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceSymposium on Advances in Mathematical Logic, SAML 2018
Country/TerritoryJapan
CityKobe
Period18/9/1818/9/20

Keywords

  • Regularity properties of sets of reals
  • Stationary tower

ASJC Scopus subject areas

  • Mathematics(all)

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