A note on strong negative partition relations

Details A note on strong negative partition relations A note on strong negative partition relations

2007-03-21

arxiv.org/abs/math/0703647v2

Mathematics

Logic

23 pages. Covers my talk at the AMS meeting at Miami University. This is essentially in final form, and is more than twice the

Scientific paper

We analyze a natural function definable from a scale at a singular cardinal, and using this function we are able to obtain quite 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.

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