Combinatorial Aspects of the Splitting Number

TL;DR

This paper introduces the strong splitting number, establishes its equivalence to the splitting number when it exists, and explores conditions under which this number can be a singular cardinal.

Contribution

It defines the strong splitting number and proves its equality to the splitting number, providing new insights into their relationship and restrictions on singular cardinal values.

Findings

Strong splitting number equals the splitting number when it exists.

Restrictions on the possibility of the splitting number being a singular cardinal.

Abstract

We define the strong splitting number, prove that it equals s when exists, and put some restrictions on the possibility that s is a singular carcinal.