We analyze a natural function definable from a scale at a singular cardinal, and use it to obtain some strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main result makes use of club-guessing, and as a corollary we obtain a fairly easy proof of a difficult result of Shelah connecting weak saturation of a certain club-guessing ideal with strong failures of square-brackets partition relations. We then investigate the strength of weak saturation of such ideals and obtain some results on stationary reflection.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-1,
author = {Todd Eisworth},
title = {A note on strong negative partition relations},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {97-123},
zbl = {1168.03034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-1}
}
Todd Eisworth. A note on strong negative partition relations. Fundamenta Mathematicae, Tome 205 (2009) pp. 97-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-1/