### 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 motivatedby 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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