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Converse dual cardinals. (English) Zbl 1102.03048
The authors investigate the structure \(((\omega), <^*)\) where \((\omega)\) denotes the set of all partitions of the set of natural numbers and \(A <^*B\) means that the partition \(A\) is coarser than the partition \(B\). They determine the values of some cardinals which are associated in a natural way with the corresponding cardinal invariants of the continuum. These cardinals are the so-called dual cardinals. They are interested especially in the almost disjointness number and the tower number. They propose to redefine the tower number in a more natural way.

MSC:
03E17 Cardinal characteristics of the continuum
03E05 Other combinatorial set theory
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