Geodesic
Cardinal invariants of the lattice of partitions
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 543-558.

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We study cardinal coefficients related to combinatorial properties of partitions of $\omega$ with respect to the order of almost containedness.
Classification : 03E05, 03E35
Keywords: lattice of partitions; almost containedness; tower number; splitting number; reaping number; Cohen's forcing 
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Majcher-Iwanow, Barbara. Cardinal invariants of the lattice of partitions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 543-558. http://geodesic.mathdoc.fr/item/CMUC_2000__41_3_a10/