Third Hausdorff Medal 2017

Ladies and gentlemen, dear friends and colleagues!

It is my honor and pleasure to announce the winner of the third Hausdorff medal of the European Set Theory Society. The Hausdorff medal is awarded biennially (i.e. once every second year) for the most influential work in set theory published in the five years preceding the awarding of the medal. The prize committee, that consists of the members of the Board of Trustees of the Society, decided that the third Hausdorff medal is awarded to Maryanthe Malliaris and Saharon Shelah for their work outlined in the paper:

General topology meets model theory, on p and t. Proc. Natl. Acad. Sci. USA 110 (2013), no. 33, 13300-13305,

and then expounded in the detailed, 60 page long version:

Cofinality spectrum theorems in model theory, set theory, and general topology. J. Amer. Math. Soc. 29 (2016), no. 1, 237-297.

LAUDATION:

Malliaris and Shelah solved two long-standing and fundamental problems:

First, they solved a more than 50 year old set theoretic problem, going back to Rothberger, by showing that the well-known and important cardinal characteristics p and t of the continuum are actually equal.

Secondly, they solved a 40 year old problem in model theory by showing that the maximality in Keislers order is not characterized by the strict order property, but that a weak order property called SOP2 suffices.

Both results follow from a brilliant analysis of definability in ultraproducts of finite linear orders. This analysis is also unique in proving that there are theories more complex than the stable, i.e. minimal theories but less complex than the maximal class in Keisler’s order.

To conclude, this important work of Malliaris and Shelah opens the door for significant and fruitful new interactions between set theory and model theory.