PFA(S) [S] and countably compact spaces

被引：3

作者：

Dow, Alan ^{[1
]}

Tall, Franklin D. ^{[2
]}

机构：

[1] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

TOPOLOGY AND ITS APPLICATIONS | 2017年 / 230卷

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Locally compact; Normal; Countably compact; Free sequence; Countably tight; Coherent Souslin tree; PFA(S) [S; Perfect pre-image of omega(1); Paracompact; Sequentially compact; SOUSLIN TREE;

D O I：

10.1016/j.topol.2017.08.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S) [S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：393 / 416

页数：24

共 29 条

[1]

Arhangelskii A. V., 1968, MICH MATH J, V15, P506

[2]

ARHANGELSKII AV, 1968, MICH MATH J, V15, P313

[3]

Balogh Z., 1983, COMMENT MATH U CAROL, V24, P63

[4] ON THE CONSISTENCY OF THE MOORE-MROWKA SOLUTION [J].

DOW, A .

TOPOLOGY AND ITS APPLICATIONS, 1992, 44 (1-3) :125-141

[5]

Dow A., 2017, CAN J MATH

[6]

Dow A., 2013, RECENT PROGR GEN TOP, VIII, P329

[7]

Dow A., HEREDITARILY N UNPUB

[8] On perfect pre-images of ω1 [J].

Eisworth, T .

TOPOLOGY AND ITS APPLICATIONS, 2002, 125 (02) :263-278

[9] Forcing with a coherent Souslin tree and locally countable subspaces of countably tight compact spaces [J].

Fischer, A. J. ;

Tall, F. D. ;

Todorcevic, S. .

TOPOLOGY AND ITS APPLICATIONS, 2015, 195 :284-296

[10]

FLEISSNER W, 1974, P AM MATH SOC, V46, P294, DOI 10.2307/2039914

← 1 2 3 →