Forcing techniques for Cichoń's Maximum: Lecture notes for the mini-course at the University of Vienna (2402.11852v3)

Abstract: Cicho\'n's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's, Goldstern, Kellner and Shelah constructed a forcing model of Cicho\'n's Maximum (meaning that all non-dependent cardinal characteristics are pairwise different) by using large cardinals. Some years later, we eliminated this large cardinal assumption. In this mini-course, we explore the forcing techniques to construct the Cicho\'n's Maximum model and much more.