A note on some versions of club

Abstract

This note gives two results on guessing unbounded subsets of lambda^+. The first is a positive result and applies to the situation of lambda regular, while the second is a negative consistency result which applies to the situation of lambda singular. Both results are connected to an earlier result of the same authors in which they showed that a certain version of clubsuit holds at a successor of singular just in ZFC. The first result here shows that that fact can to a certain extent be extended to the successor of singular. The negative result here gives limitations to the extent to which one can hope to extend the afore mentioned fact. This note is presently only available as an electronic publication. It can be obtained as a ps file either from the e-prints archive, or from the authors' home pages.