12 January, Thursday 14.15-15.45, Mathematical institute, University of Bonn, room 0.011

Benjamin Miller (Universität Münster): Local rigidity, Glimm-Effros embeddings, and definable cardinals

Abstract: We employ local rigidity properties of the usual action of GL_2(Z) on the torus to rule out analogs of the Glimm-Effros dichotomy for non-measure-hyperfinite equivalence relations. As a consequence, we obtain the best possible bounds obtainable through

measure-theoretic means concerning the region in which the definable cardinals become non-linear. I hope to make the talk accessible to a broad mathematical audience.

20 January, Friday 10.15-11.45, Mathematical institute, University of Bonn, room 1.012 (Hausdorffraum)

Marcos Cramer (Universität Bonn): Ackermann set theory and function theory

We present Ackermann set theory, a conservative extension of ZF with classes. Our motivation for considering this theory comes from a certain construction in mathematical texts – the implicit introduction of function – that we aim to capture formally. A function f can be introduced implicitly by a construct of the form: “For every x there is an f(x) such that R(x,f(x)).” Implicit introduction of functions gives rise to a paradox similar to Russell’s paradox. In order to avoid this paradox, we have developed a theory of functions that closely resembles Ackermann set theory. We show that this theory is equiconsistent to ZFC.

24 January, Tuesday 16.30-18.00, Mathematical institute, University of Bonn, room 0.003

Stefan Geschke (Universität Bonn): There is no universal clopen graph on a compact metric space

Slides of Ben Miller’s talk on January 12th.

Ben Miller – Local rigidity, Glimm-Effros embeddings, and definable cardinals.pdf