  We generalize the combinatorial principles $C_n(\kappa), C^s_n(\kappa)$ and
$Princ(\kappa)$ introduced by various authors, and prove some of their
properties and connections between them. We also answer a question asked by
Juhasz-Kunen about the relation between these principles, by showing that
$C_n(\kappa)$ does not imply $C_{n+1}(\kappa)$, for any $n>2$. We also show the
consistency of $C(\kappa)+\neg C^s(\kappa).$
