Kurt Gödel Research Center

2020 seminar talk: Ramsey-like Operators

Talk held by Peter Holy (University of Udine, Italy) at the KGRC seminar on 2020-12-17.

Abstract

Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations.

The slides for this talk are available.

Time and Place

Talk at 3:00pm via Zoom