On $C_n^s(\kappa )$ and the Juhasz-Kunen question

Abstract

We generalize the combinatorial principles $C_n(\kappa ),C_n^s(\kappa )$ 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 $C(\kappa )+\neg C^s(\kappa ).$

This is publication 1125 of second author