https://ests.wordpress.com/2023/09/04/two-mini-courses-in-set-theory-univers...
The University of Vienna Set Theory Research Seminar will host two mini-courses in hybrid format in the coming Winter Semester 2023.
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1) Title: Convergence in Banach spaces of measures and cardinal characteristics of the continuum Damian Sobota (FWF ESPRIT Project Leader, University of Vienna)
When and where: Thursdays (05.10.2023-23.11.2023, 6 lectures) 11:30-13:00, Seminarraum 10, Kolingasse 14-16, Uni Wien
Zoom Meeting ID: 210 955 0387, Passcode: kgrc https://univienna.zoom.u/j/2109550387?pwd=ZXZMLzZIWERXK2lnWlROZncxQkVSUT09 https://univienna.zoom.us/j/2109550387?pwd=ZXZMLzZIWERXK2lnWlROZncxQkVSUT09
Abstract: During this mini-course I will show how various properties of Banach spaces of measures (on compact spaces or Boolean algebras) are affected by values of the cardinal characteristics of the continuum occuring in Cichoń’s diagram and van Douwen’s diagram. We will in particular be interested in convergence properties of sequences of measures in weak* and weak topologies. Besides, we will study what impact extending the set-theoretic universe by forcing can have on topologies of ground model Banach spaces of measures. Finally, I will present connections between convergence of measures on compact spaces and filters on countable sets.
2) Title: Forcing techniques for Cichoń’s Maximum Diego A. Mejía (Associate Professor, Shizuoka University)
When and where: Thursdays (30.11.2023-25.01.2024, 6 lectures) 11:30-13:00, Seminarraum 10, Kolingasse 14-16, Uni Wien
Zoom Meeting ID: 210 955 0387, Passcode: kgrc https://univienna.zoom.us/j/2109550387?pwd=ZXZMLzZIWERXK2lnWlROZncxQkVSUT09
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 decade, 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. Concretely, we discuss the following components: 1. Tukey connections and cardinal characteristics of the continuum 2. Review of FS (finite support) iterations and basic methods to modify cardinal characteristics. 3. Preservation theory for cardinal characteristics. 4. FS iterations with measures and ultrafilters on the natural numbers. 5. Boolean Ultrapowers. 6. Forcing Intersected with submodels.
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For further information, please write to vera.fischer@univie.ac.at.