STICKS AND CLUBS

We study combinatorial principles known as stick and club. Several var iants of these principles and cardinal invariants connected to them ar e also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, w e give several generic extensions where some of these principles hold together with -CH and Martin's axiom for countable p.o.-sets. An itera tive version of the pseudo-product is used under an inaccessible cardi nal to show the consistency of the club principle for every stationary subset of limits of omega(1) together with (sic)CH and Martin's axiom for countable p.o.-sets.