On Countable Stationary Towers

Yo Matsubara; Toshimichi Usuba

doi:10.1007/978-981-16-4173-2_6

On Countable Stationary Towers

Yo Matsubara^*, Toshimichi Usuba

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions
Editors	Toshiyasu Arai, Makoto Kikuchi, Satoru Kuroda, Mitsuhiro Okada, Teruyuki Yorioka
Publisher	Springer
Pages	133-141
Number of pages	9
ISBN (Print)	9789811641725
DOIs	https://doi.org/10.1007/978-981-16-4173-2_6
Publication status	Published - 2021
Event	Symposium on Advances in Mathematical Logic, SAML 2018 - Kobe, Japan Duration: 2018 Sept 18 → 2018 Sept 20

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	369
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Symposium on Advances in Mathematical Logic, SAML 2018
Country/Territory	Japan
City	Kobe
Period	18/9/18 → 18/9/20

Keywords

Regularity properties of sets of reals
Stationary tower

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-981-16-4173-2_6

Cite this

Matsubara, Y., & Usuba, T. (2021). On Countable Stationary Towers. In T. Arai, M. Kikuchi, S. Kuroda, M. Okada, & T. Yorioka (Eds.), Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions (pp. 133-141). (Springer Proceedings in Mathematics and Statistics; Vol. 369). Springer. https://doi.org/10.1007/978-981-16-4173-2_6

On Countable Stationary Towers. / Matsubara, Yo; Usuba, Toshimichi.
Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions. ed. / Toshiyasu Arai; Makoto Kikuchi; Satoru Kuroda; Mitsuhiro Okada; Teruyuki Yorioka. Springer, 2021. p. 133-141 (Springer Proceedings in Mathematics and Statistics; Vol. 369).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Matsubara, Y & Usuba, T 2021, On Countable Stationary Towers. in T Arai, M Kikuchi, S Kuroda, M Okada & T Yorioka (eds), Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions. Springer Proceedings in Mathematics and Statistics, vol. 369, Springer, pp. 133-141, Symposium on Advances in Mathematical Logic, SAML 2018, Kobe, Japan, 18/9/18. https://doi.org/10.1007/978-981-16-4173-2_6

Matsubara, Yo ; Usuba, Toshimichi. / On Countable Stationary Towers. Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions. editor / Toshiyasu Arai ; Makoto Kikuchi ; Satoru Kuroda ; Mitsuhiro Okada ; Teruyuki Yorioka. Springer, 2021. pp. 133-141 (Springer Proceedings in Mathematics and Statistics).

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On Countable Stationary Towers

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