# Sh:768

• Shelah, S., & Tsaban, B. (2003). Critical cardinalities and additivity properties of combinatorial notions of smallness. J. Appl. Anal., 9(2), 149–162.
• Abstract:
Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (\tau-covers). We deal with two types of combinatorial questions which arise from this study.

(a) Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of the continuum.

(b) We study the additivity numbers of the combinatorial notions corresponding to the topological diagonalization notions.

This gives new insights on the structure of the eventual dominance ordering on the Baire space, the almost inclusion ordering on the Rothberger space, and the interactions between them.

• published version (14p)
Bib entry
@article{Sh:768,
author = {Shelah, Saharon and Tsaban, Boaz},
title = {{Critical cardinalities and additivity properties of combinatorial notions of smallness}},
journal = {J. Appl. Anal.},
fjournal = {Journal of Applied Analysis},
volume = {9},
number = {2},
year = {2003},
pages = {149--162},
issn = {1425-6908},
mrnumber = {2021285},
mrclass = {03E17 (03E05 03E35)},
doi = {10.1515/JAA.2003.149},
note = {\href{https://arxiv.org/abs/math/0304019}{arXiv: math/0304019}},
arxiv_number = {math/0304019}
}