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

Abstract

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.

Lecture notes corresponding to a mini-course of six sessions at the University of Vienna, from November 30th, 2023 to January 25th, 2024. More details have been added to the second version; typos corrected for the third (and final) version