Club-guessing, stationary reflection, and coloring theorems

We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.Comment: Initial public versio

Galvin's Conjecture and Weakly Precipitous Ideals

We show that the Raghavan-Todor\v{c}evi\'{c} proof of a longstanding conjecture of Galvin from Woodin cardinals can be carried out under weaker assumptions that follow from the existence of Ramsey cardinals, and that do not imply the existence of $0^\sharp$.Comment: First public draf