Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal
Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 287-296
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
By an $ω_1$- tree we mean a tree of power $ω_1$ and height $ω_1$. Under CH and $2^{ω_{1}} > ω_2$ we call an $ω_1$-tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between $ω_1$ and $2^{ω_{1}}$. In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus $2^{ω_{1}} > ω_2$ that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus $2^{ω_{1}} = ω_4$ that there only exist Kurepa trees with $ω_{3}$-many branches, which answers another question of [Ji2].
@article{10_4064_fm_141_3_287_296,
author = {Saharon Shelah and R. Jin},
title = {Planting {Kurepa} trees and killing {Jech-{\CYRK}unen} trees in a model by using one inaccessible cardinal},
journal = {Fundamenta Mathematicae},
pages = {287--296},
year = {1992},
volume = {141},
number = {3},
doi = {10.4064/fm-141-3-287-296},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-141-3-287-296/}
}
TY - JOUR AU - Saharon Shelah AU - R. Jin TI - Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal JO - Fundamenta Mathematicae PY - 1992 SP - 287 EP - 296 VL - 141 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-141-3-287-296/ DO - 10.4064/fm-141-3-287-296 LA - en ID - 10_4064_fm_141_3_287_296 ER -
%0 Journal Article %A Saharon Shelah %A R. Jin %T Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal %J Fundamenta Mathematicae %D 1992 %P 287-296 %V 141 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/fm-141-3-287-296/ %R 10.4064/fm-141-3-287-296 %G en %F 10_4064_fm_141_3_287_296
Saharon Shelah; R. Jin. Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal. Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 287-296. doi: 10.4064/fm-141-3-287-296
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