On $C^s_n(\kappa)$ and the Juhasz-Kunen question

by Golshani and Shelah. [GsSh:1125]

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)+ not C^s(kappa).

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