### Strongly almost disjoint sets and weakly uniform bases

by Balogh and Davis and Just and Shelah and Szeptycki. [BDJShS:674]

Transactions AMS, 2000

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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