Social welfare relation and irregular sets
Mittwoch, 3.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Zame and Lauwers recently showed connections between set theory\nand theoretical economics. In particular they showed that the existence of\nsocial welfare relations satisfying intergenerational equity imply the\nexistence of non-constructible objects, such as non-Ramsey and non-measurable\nsets. In this talk I prove some connection also with another popular\nregularity property, i.e., the Baire property, and if there is any time left\nI propose to use Shelah's amalgamation in order to show that the two above\nimplications does not reverse.
What can be expressed in first-order logic with bounded quantifier rank and why do we want to know that?
Mittwoch, 10.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Ultrametric spaces, isometry, and isometry groups
Mittwoch, 17.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Gao and Kechris proposed in 2003 two somewhat related problems\nconcerning ultrametric spaces, namely:\n\n1) Determine the complexity of the isometry relation on locally compact\nPolish ultrametric spaces.\n\n2) Characterize the Polish groups that are isomorphic (as topological\ngroups) to the isometry group of some Polish ultrametric space.\n\nWe will present a construction strictly relating ultrametric spaces and a\nspecial kind of trees which helps in tackling these two problems. This\ntechnique applies to both separable and non-separable complete ultrametric\nspaces, and allows us to e.g. show that they are unclassifyiable up to\nisometry even when considering only discrete spaces. (Joint work with R.\nCamerlo and A. Marcone.)\n
Neeman-Forcing
Mittwoch, 24.5.17, 16:30-17:30, Raum 404, Eckerstr. 1