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
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>.