The University of Vienna Set Theory Research Seminar will host the following mini-course in hybrid format in the coming Winter Semester 2023.
Mini-course: Forcing techniques for Cichon's Maximum by Diego Mejia (Shizuoka University)
Thursdays (6 lectures) Japan Standart Time 19:30-21:00 (Central European Time 11:30-13:00) Nov 30th-Dec 14th; Jan 11th-25th
Seminarraum 10, Kolingasse 14-16, Uni Wien
Zoom Meeting ID: 210 955 0387, Passcode: kgrc https://univienna.zoom.us/j/2109550387?pwd=ZXZMLzZIWERXK2lnWlROZncxQkVSUT09
Abstract: Cichon’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 decade, Goldstern, Kellner and Shelah constructed a forcing model of Cichon’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 Cichon’s Maximum model and much more. Concretely, we discuss the following components:
1. (Nov 30th) Tukey connections and cardinal characteristics of the continuum 2. (Dec 7th) Review of FS (finite support) iterations and basic methods to modify cardinal characteristics. 3. (Dec 14th) Preservation theory for cardinal characteristics. 4. (Jan 11th) FS iterations with measures and ultrafilters on the natural numbers. 5. (Jan 18th) Boolean Ultrapowers. 6. (Jan 25th) Forcing Intersected with submodels.