A note on strong negative partition relations
Tom 202 / 2009
Fundamenta Mathematicae 202 (2009), 97-123
MSC: Primary 03E02.
DOI: 10.4064/fm202-2-1
Streszczenie
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.
