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On compact separable radial spaces

  Published:1997-12-01
 Printed: Dec 1997
  • Alan Dow
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Abstract

If ${\cal A} $ and ${\cal B}$ are disjoint ideals on $\omega$, there is a {\it tower preserving\/} $\sigma$-centered forcing which introduces a subset of $\omega$ which meets every infinite member of ${\cal A}$ in an infinite set and is almost disjoint from every member of ${\cal B}$. We can then produce a model in which all compact separable radial spaces are Fr\'echet, thus answering a question of P.~Nyikos. The question of the existence of compact ccc radial spaces which are not Fr\'echet was first asked by Chertanov (see \cite{Ar78}).
MSC Classifications: 54D30 show english descriptions Compactness 54D30 - Compactness
 

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