Talks and presentations

Strong compactness and the continuum function

July 24, 2018

Talk, University of Udine, Udine, Italy

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 and Woodin-like cardinals

July 18, 2018

Talk, University of Leeds, Leeds, UK

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. I argue that this naturally leads to the definition of a new type of large cardinal, called “Woodin for strong compactness” and discuss some of its properties that arose during my PhD research.

Cardinal characteristics and strong compactness

January 30, 2018

Talk, Winter School 2018, Hejnice, Czech Republic

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. I talked about an application of this, which is that it is possible to collapse any supercompact cardinal to a non-supercompact strongly compact cardinal and still be able to fully control its ultrafilter number.