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resolvability; irresolvability; Martin's Axiom; a space of weight less than $\frak C$
We construct in Bell-Kunen's model: (a) a group maximal topology on a countable infinite Boolean group of weight $\aleph_1 < {\frak C}$ and (b) a countable irresolvable dense subspace of $2^{\omega_1}$. In this model ${\frak C}=\aleph_{\omega_1}$.
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