Type: Article
Publication Date: 1993-01-01
Citations: 2
DOI: https://doi.org/10.1090/s0002-9947-1993-1196219-6
A model of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ZFC"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>ZFC</mml:mtext> </mml:mrow> <mml:annotation encoding="application/x-tex">{\text {ZFC}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is constructed in which there exists a subset of the Moore plane that is countably paracompact but not normal. The method used in the construction is forcing using uncountable sets of finite partial functions, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ω<!-- ω --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\omega _1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega 2"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ω<!-- ω --></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\omega _2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are shown to be preserved using a fusion lemma.