# Stephen Jackson: New partition results from AD

Week 1, Wednesday June 17, 10:00-10:50

We obtain two new partition properties from AD. The first result (joint with A. Apter and B. Löwe) is that for every inaccessible Suslin cardinal $\kappa$ we have the polarized partition property
(kappa,kappa^+,kappa^++) -> (kappa,kappa^+,kappa^++)^(kappa,kappa,kappa)
This was used to obtain the consistency relative to ZF of the possible patters of cofinalities of the first three uncountable cardinals.
The second result pins down the exact partition properties of the regular cardinals below the projective ordinals.