Sticks and clubs

Sakaé Fuchino; Saharon Shelah; Lajos Soukup

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arXiv · math/9804153

Sticks and clubs

Sakaé Fuchino·Saharon Shelah·Lajos Soukup

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Abstract

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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BibTeX RIS

Sakaé Fuchino, Saharon Shelah, Lajos Soukup. 1998-04-15. Sticks and clubs. https://arxiv.org/abs/math/9804153

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