# Sh:1032

• Machura, M., Shelah, S., & Tsaban, B. (2016). The linear refinement number and selection theory. Fund. Math., 234(1), 15–40.
• Abstract:
The linear refinement number \mathfrak{lr} is a combinatorial cardinal characteristic of the continuum. This number, which is a relative of the pseudointersection number \mathfrak{p}, showed up in studies of selective covering properties, that in turn were motivated by the tower number \mathfrak{t}.

It was long known that \mathfrak{p}=\min\{\mathfrak{t},\mathfrak{lr}\} and that \mathfrak{lr}\le\mathfrak{d}. We prove that if \mathfrak{lr}=\mathfrak{d} in all models where the continuum is \aleph_2, and that \mathfrak{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.

• Current version: 2015-06-18_11 (22p) published version (26p)
Bib entry
@article{Sh:1032,
author = {Machura, Micha{\l} and Shelah, Saharon and Tsaban, Boaz},
title = {{The linear refinement number and selection theory}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {234},
number = {1},
year = {2016},
pages = {15--40},
issn = {0016-2736},
mrnumber = {3509814},
mrclass = {03E17 (03E75 54C65)},
doi = {10.4064/fm124-8-2015},
note = {\href{https://arxiv.org/abs/1404.2239}{arXiv: 1404.2239}},
arxiv_number = {1404.2239}
}