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

Cichoń’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 Cichoń’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 Cichoń’s Maximum model and much more.