Refining systems of mad families

Abstract

AbstractWe construct a model in which there exists a refining matrix of regular height λ larger than $$\mathfrak{h}$$ h ; both $$\lambda = \mathfrak{c}$$ λ = c and $$\lambda < \mathfrak{c}$$ λ < 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.