Similar but not the same: various versions of $\clubsuit$ do not coincide

by Dzamonja and Shelah. [DjSh:574]
J Symbolic Logic, 1999
We consider various versions of the clubsuit principle. This principle is a known consequence of diamondsuit . It is well known that diamondsuit is not sensitive to minor changes in its definition, e.g. changing the guessing requirement form ``guessing exactly'' to ``guessing modulo a finite set''. We show however, that this is not true for clubsuit . We consider some other variants of clubsuit as well.

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