# Sh:544

• Fuchino, S., Shelah, S., & Soukup, L. (1997). Sticks and clubs. Ann. Pure Appl. Logic, 90(1-3), 57–77.
• 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 \neg 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 \neg CH and Martin’s Axiom for countable p.o.-sets.
• Current version: 1998-04-20_10 (24p) published version (21p)
Bib entry
@article{Sh:544,
author = {Fuchino, Saka{\'e} and Shelah, Saharon and Soukup, Lajos},
title = {{Sticks and clubs}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {90},
number = {1-3},
year = {1997},
pages = {57--77},
issn = {0168-0072},
mrnumber = {1489304},
mrclass = {03E55 (03E05 03E35)},
doi = {10.1016/S0168-0072(97)00030-4},
note = {\href{https://arxiv.org/abs/math/9804153}{arXiv: math/9804153}},
arxiv_number = {math/9804153}
}