Abstract: Generic large cardinals are one of the main approaches to Gödel's Program to find extensions of the axioms of set theory to answer independent questions such as the Continuum Hypothesis. These are small versions of large cardinals that have a more direct impact on ordinary mathematical objects. This Habilitation Thesis presents the author's work on mapping out the capabilities and limitations of these axioms, culminating in a recent result with Yair Hayut that a natural and provably maximal such axiom, a global assertion about ideals of small density, is consistent relative to traditional large cardinals. This axiom also solves several problems in infinitary combinatorics. Several other directions in the generic large cardinal world are also explored, including the tree property, maximal independent families, and Chang's conjectures.
Generic Large Cardinals
30.09.2025 09:30 - 10:15
Organiser:
G. Teschl (U Wien), R. I. Bot (U Wien)
Location: