Generalized side-conditions and Moore-Mrówka

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• 作者：Alan Dow¹ ; ^{adow@uncc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54A20 ; 54G20 ; 54A35 ; 03E35 ; 54G12
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：197
• 期：Complete
• 页码：75-101
• 全文大小：696 K

文摘

We prove that it is consistent (even with Martin's Axiom) that there is first-countable initially 237718c3" title="Click to view the MathML source">ω₁${\omega }_1$-compact space with cardinality greater than the continuum. We also prove that it is consistent with Martin's Axiom and c=ω₂$\mathfrak{c}={\omega }_2$ that there is a compact space of countable tightness which is not sequential. It is known that neither statement is consistent with the Proper Forcing Axiom. We use an innovative new method of constructing proper posets with elementary submodels as side conditions introduced by Neeman.