Refining systems of mad families

We construct a model in which there exists a refining matrix of regular height λ larger than \(\mathfrak{h}\) $$\mathfrak{h}$$ ; both \(\lambda = \mathfrak{c}\) $$\lambda =\mathfrak{c}$$ and \(\lambda < \mathfrak{c}\) $$\lambda <\mathfrak{c}$$ are possible. A refining matrix is a refining system of mad families without common refinement. Of particular interest in our proof is the preservation of \({\cal B}\) $$ℬ$$ -Canjarness.