Talks

In Hilbert’s famous list of problems for mathematicians in the 20th century, the first one was to resolve the Continuum Hypothesis, namely to determine the exact size of the set of real numbers.

This is a contributed talk at the second day of the Logic Colloquium 2018, which was hosted by the University of Udine in Italy. I talked about work in progress with Arthur Apter on the problem of controlling the continuum function in the presence of strongly compact cardinals.

Vopěnka’s Principle has evolved into one of the strongest connections among category theory, model theory and set theory. In this talk, I give a brief overview of the historical development of the principle, show some of its numerous characterisations and contrast it with large cardinal notions from set theory, especially with Woodin cardinals.

In this talk, I presented a part of my thesis which had to do with controlling the cardinal characteristics of strongly compact cardinals. I focused on the ultrafilter number, due to the recent progress made by Brooke-Taylor, Fischer, Friedman and Montoya who showed that it is possible to fully control the value of the ultrafilter number of a supercompact cardinal.