Uncountable intersections of open sets under CPA_{prism}
by
Krzysztof Ciesielski,
and Janusz Pawlikowski
Proc. Amer. Math. Soc. 132(11) (2004), 33793385.
We prove that the Covering Property Axiom CPA_{prism},
which holds in the iterated perfect set model, implies the following facts.

If G is an intersection of \omega_{1}many open sets
of a Polish space and G has cardinality continuum then G contains a perfect set.

There exists a subset G of the Cantor set
which is an intersection of \omega_{1}many open sets
but is not a union of \omega_{1}many closed sets.
The example from the second fact refutes a conjecture of Brendle, Larson, and Todorcevic.\omega_{1}<\continuum.
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Last modified July 20, 2004.