Refining systems of mad families

Abstract

We construct a model in which there exists a refining matrix of regular height λ larger than \(\mathfrak{h}\); both \(\lambda = \mathfrak{c}\) and \(\lambda < \mathfrak{c}\) 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 \({\cal B}\)-Canjarness.