### Sticks and clubs

by Fuchino and Shelah and Soukup. [FShS:544]

Annals Pure and Applied Logic, 1997

We study combinatorial principles known as stick and
club. Several variants of these principles and cardinal invariants
connected to them are also considered. We introduce a new kind of
side-by-side product of partial orders which we call
pseudo-product. Using such products, we give several generic
extensions where some of these principles hold together with not
CH and Martin's Axiom for countable p.o.-sets. An iterative version
of the pseudo-product is used under an inaccessible cardinal to show
the consistency of the club principle for every stationary subset of
limits of omega_1 together with not CH and Martin's Axiom for
countable p.o.-sets.

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