Martin's axiom and almost disjoint families

Abstract

Assuming $\rfs{MA} + \aleph_1 < 2^{\aleph_0}$, we show that, for any $\kappa,\lambda < 2^{\aleph_0}$ and any almost disjoint family $\setn{a_i}{i < \lambda}$ of countable subsets of $\kappa$, with $\lambda < 2^{\aleph_0}$, there is a partition $\setn{p_n}{n\in\omega}$ of $\kappa$ so that $p_n \cap a_i$ is finite for each $(i,n) \in \lambda\times \omega$