English

Sticks and clubs

Logic 2016-09-07 v1

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.

Keywords

Cite

@article{arxiv.math/9804153,
  title  = {Sticks and clubs},
  author = {Sakaé Fuchino and Saharon Shelah and Lajos Soukup},
  journal= {arXiv preprint arXiv:math/9804153},
  year   = {2016}
}
R2 v1 2026-07-22T17:58:26.473Z