The linear refinement number and selection theory

by Machura and Shelah and Tsaban. [MaShTs:1032]
Fundamenta Math, 2016
The linear refinement number {lr} is a combinatorial cardinal characteristic of the continuum. This number, which is a relative of the pseudointersection number {p}, showed up in studies of selective covering properties, that in turn were motivated

by the tower number {t} . It was long known that {p}= min {{t}, {lr}} and that {lr} <= {d} . We prove that if {lr}= {d} in all models where the continuum is aleph_2, and that {lr} is not provably equal to any classic combinatorial cardinal characteristic of the continuum. These results answer several questions from the theory of selection principles.


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