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# Sequential Order Under PFA

Published:2010-08-26
Printed: Jun 2011
• Alan Dow,
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.
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## Abstract

It is shown that it follows from PFA that there is no compact scattered space of height greater than $\omega$ in which the sequential order and the scattering heights coincide.
 Keywords: sequential order, scattered spaces, PFA
 MSC Classifications: 54D55 - Sequential spaces 03E05 - Other combinatorial set theory 03E35 - Consistency and independence results 54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)