The cardinal invariants h, b, s of Ppωq are known to satisfy that ω1 ď h ď mintb, su. We prove that all inequalities can be strict. We also introduce a new upper bound for h and show that it can be less than s. The key method is to utilize finite support matrix iterations of ccc posets following [4].

Using a finite support iteration of ccc posets, if μ is a measurable cardinal and μ < κ < λ, then using similar techniques the authors obtain the consistency of .Expand

Abstract If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every… Expand

It is consistent, relative to ZFC, that the minimum number of subsets ofω generating a non-principal ultrafilter is strictly smaller than the dominating number. In fact, these two numbers can be any… Expand

Using matrix iterations of ccc posets, it is proved that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.Expand

A forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets is introduced, which are referred to as 3D-coherent systems.Expand

Abstract We prove the consistency of $$~~\text{add}\left( \mathcal{N} \right)<\operatorname{cov}\left( \mathcal{N} \right)<\mathfrak{p}\text{=}\mathfrak{s}\text{=}\mathfrak{g}< \text{add}\left(… Expand