Similar but not the same: various versions of club do not coincide

A note on some versions of club

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 …