250086 VO Selected topics in set theory (2014S)

This course will focus on cardinal characteristics for uncountable regular cardinals. This is a relatively new subject with many interesting open questions. There are at least four motivations for pursuing this topic: It fuels the search for new iterated forcing methods using uncountable support, it interacts in interesting ways with large cardinal theory, the global behaviour of cardinal characteristics gives rise to the study of "internal consistency" in set theory and it provides a context where analogues of unsolved problems for the standard cardinal characteristics may be solved (for example Roitman's problem). We'll look at the dominating and bounding numbers, the almost disjointness number, the uniformity number and the splitting number for uncountable regular cardinals, touching on work of Cummings-Shelah, Blass-Hyttinen-Zhang, Garti-Shelah, Ben-Neria and joint work of mine with Honzik, Ondrejovic, Thompson and Zdomskyy.