I[o2] can be the nonstationary ideal on Cof(o1)
作者： William J. Mitchell
DOI: 10.1090/S0002-9947-08-04664-3
关键词: If and only if 、 Ideal (set theory) 、 Mathematics 、 Mahlo cardinal 、 Pure mathematics
摘要: We answer a question of Shelah by showing that it is consistent every member I[ω 2 ] n Cof(ω 1 ) nonstationary if and only there κ + -Mahlo cardinal K.
unirioja.es
ams.org
sci-hub.se 参考文章(13)
Sy-David Friedman, Forcing with Finite Conditions Set theory. pp. 285- 295 ,(2006) , 10.1007/3-7643-7692-9_10
James E. BAUMGARTNER, Applications of the Proper Forcing Axiom Handbook of Set-Theoretic Topology. pp. 913- 959 ,(1984) , 10.1016/B978-0-444-86580-9.50024-0
Uri Abraham, Aronszajn trees on ℵ2 and ℵ3 Annals of Pure and Applied Logic. ,vol. 24, pp. 213- 230 ,(1983) , 10.1016/0168-0072(83)90006-4
William J. Mitchell, On the Hamkins approximation property Annals of Pure and Applied Logic. ,vol. 144, pp. 126- 129 ,(2006) , 10.1016/J.APAL.2006.05.005
Saharon Shelah, Reflecting stationary sets and successors of singular cardinals Archive for Mathematical Logic. ,vol. 31, pp. 25- 53 ,(1991) , 10.1007/BF01370693
William J. Mitchell, Adding Closed Unbounded Subsets of ω₂ with Finite
Forcing Notre Dame Journal of Formal Logic. ,vol. 46, pp. 357- 371 ,(2005) , 10.1305/NDJFL/1125409334
William Mitchell, Aronszajn trees and the independence of the transfer property Annals of Mathematical Logic. ,vol. 5, pp. 21- 46 ,(1972) , 10.1016/0003-4843(72)90017-4
Stevo Todorčevi{ć, Directed sets and cofinal types Transactions of the American Mathematical Society. ,vol. 290, pp. 711- 723 ,(1985) , 10.1090/S0002-9947-1985-0792822-9
JINDRICH ZAPLETAL, Characterization of the Club Forcing Annals of the New York Academy of Sciences. ,vol. 806, pp. 476- 484 ,(1996) , 10.1111/J.1749-6632.1996.TB49190.X
Piotr Koszmider, On strong chains of uncountable functions Israel Journal of Mathematics. ,vol. 118, pp. 289- 315 ,(2000) , 10.1007/BF02803525