# Sh:962

• Garti, S., & Shelah, S. (2012). Combinatorial aspects of the splitting number. Ann. Comb., 16(4), 709–717.
• Abstract:
We prove that the existence of strong splitting families is equivalent to the failure of the polarized relation {\mathfrak{s}\choose\omega} \rightarrow {\mathfrak{s}\choose {\omega}^{1,1}_2}. We show that both directions are consistent with ZFC, and that the strong splitting number equals to the splitting number, when exists. Consequently, we can put some restriction on the possibility that \mathfrak{s} is singular.
• published version (9p)
Bib entry
@article{Sh:962,
author = {Garti, Shimon and Shelah, Saharon},
title = {{Combinatorial aspects of the splitting number}},
journal = {Ann. Comb.},
fjournal = {Annals of Combinatorics},
volume = {16},
number = {4},
year = {2012},
pages = {709--717},
issn = {0218-0006},
mrnumber = {3000439},
mrclass = {03E02 (03E40)},
doi = {10.1007/s00026-012-0154-5},
note = {\href{https://arxiv.org/abs/1007.2266}{arXiv: 1007.2266}},
arxiv_number = {1007.2266}
}