Combinatorial Aspects of the Splitting Number

Shimon Garti, Saharon Shelah

Research output: Contribution to journalArticlepeer-review


This paper deals with the splitting number s and polarized partition relations. In the first section we define the notion of strong splitting families, and prove that its existence is equivalent to the failure of the polarized relation( s ω) → ( s ω) 1,1 2. We show that the existence of a strong splitting family is consistent with ZFC, and that the strong splitting number equals the splitting number, when it exists. Consequently, we can put some restriction on the possibility that s is singular. In the second section we deal with the polarized relation under the weak diamond, and we prove that the strong polarized relation ω) → ( ω) 1,1 2 is consistent with ZFC, even when cf (2 ω1 (hence the weak diamond holds).

Original languageEnglish
Pages (from-to)709-717
Number of pages9
JournalAnnals of Combinatorics
Issue number4
StatePublished - Dec 2012


  • Mathias forcing
  • partition calculus
  • splitting number
  • weak diamond

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Combinatorial Aspects of the Splitting Number'. Together they form a unique fingerprint.

Cite this