TY - GEN

T1 - On Countable Stationary Towers

AU - Matsubara, Yo

AU - Usuba, Toshimichi

N1 - Funding Information:
Acknowledgements The first author’s research was supported by JSPS KAKENHI Grant Nos. 18K03394. The second author’s research was supported by JSPS KAKENHI Grant Nos. 18K03403 and 18K03404.
Publisher Copyright:
© 2021, Springer Nature Singapore Pte Ltd.

PY - 2021

Y1 - 2021

N2 - 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).

AB - 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).

KW - Regularity properties of sets of reals

KW - Stationary tower

UR - http://www.scopus.com/inward/record.url?scp=85124658131&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85124658131&partnerID=8YFLogxK

U2 - 10.1007/978-981-16-4173-2_6

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

M3 - Conference contribution

AN - SCOPUS:85124658131

SN - 9789811641725

T3 - Springer Proceedings in Mathematics and Statistics

SP - 133

EP - 141

BT - Advances in Mathematical Logic - Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Selected, Revised Contributions

A2 - Arai, Toshiyasu

A2 - Kikuchi, Makoto

A2 - Kuroda, Satoru

A2 - Okada, Mitsuhiro

A2 - Yorioka, Teruyuki

PB - Springer

T2 - Symposium on Advances in Mathematical Logic, SAML 2018

Y2 - 18 September 2018 through 20 September 2018

ER -