Preservation of splitting families and cardinal characteristics of the continuum

Abstract

We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń's diagram, $\mathfrak{m}(2\text{-Knaster})$, $\mathfrak{p}$, $\mathfrak{h}$, the splitting number $\mathfrak{s}$ and the reaping number $\mathfrak{r}$.

arXiv commentSection 2 was modified to correct a mistake in the proof of the existence of a suitable bi-graph

References in corpus (12)

• Covering of the null ideal may have countable cofinality
• Decisive creatures and large continuum
• Creature forcing and large continuum: The joy of halving
• Matrix iterations with vertical support restrictions
• Filter-linkedness and its effect on preservation of cardinal characteristics
• Cichoń's maximum
• Creature forcing and five cardinal characteristics in Cichoń's diagram
• Another ordering of the ten cardinal characteristics in Cichoń's diagram
• The left side of Cichoń's diagram
• Models of some cardinal invariants with large continuum
• Controlling cardinal characteristics without adding reals
• A note on "Another ordering of the ten cardinal characteristics in Cichoń's Diagram" and further remarks