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Strongly almost disjoint sets and weakly uniform bases

Zoltán Balogh·Sheldon W. Davis·Winfried Just·Saharon Shelah·Paul J. Szeptycki
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Abstract

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of Box_lambda for singular lambda is proved. CECA is used to show that certain ``almost point- < tau'' families can be refined to point- < tau families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of ``every first countable T_1-space with a weakly uniform base has a point-countable base.''

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Zoltán Balogh, Sheldon W. Davis, Winfried Just, Saharon Shelah, Paul J. Szeptycki. 1998-03-15. Strongly almost disjoint sets and weakly uniform bases. https://arxiv.org/abs/math/9803167

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