Seminar

The talk will be about a surprising recent interaction of model theory and general topology.

Cantor proved in 1874 that the continuum is uncountable, and Hilbert's first problem asks whether it is the smallest uncountable cardinal. A program arose to study cardinal invariants of the continuum, which measure the size of the continuum in various ways. By work of Godel and Cohen, Hilbert's first problem is independent of ZFC. Much work both before and since has been done on inequalities between these cardinal invariants, but some basic questions have remained open despite Cohen's introduction of forcing. The oldest and perhaps most famous of these is whether "p = t", which was proved in a special case by Rothberger 1948, building on Hausdorff 1934.  The talk will explain how work of Malliaris and Shelah on the structure of Keisler's order, a large scale classification problem in model theory, led to the solution of this problem in ZFC as well as of an a priori unrelated open question in model theory.