Large Compact Separable Spaces May all Contain βN

  title={Large Compact Separable Spaces May all Contain $\beta$N},
  author={Alan Dow},
  • A. Dow
  • Published 1 May 1990
  • Mathematics
In the Cohen model any compact separable space that does not contain ßN has cardinality at most of the continuum. In this paper we prove the theorem stated in the abstract. By the Cohen model we mean any model obtained by adjoining N2 Cohen reals to a model of GCH. We shall, in fact, show that any compact separable space of cardinality greater than the continuum c will map onto the space /' . We will see that this is equivalent to containing ßN. We freely use any notation and conventions which… 

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