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Math Colloquium
Benjamin Miller
Muenster University
Title: Definable cardinals just beyond R / Q

Abstract: Over the last several decades, a definable refinement of the usual notion of cardinality has been employed to great effect in shedding new light on many classification problems throughout mathematics. In order to best understand such applications, one must investigate the abstract nature of the definable cardinal hierarchy. It is well known that the initial segment of the hierarchy below R / Q looks quite similar to the usual cardinal hierarchy. On the other hand, if one moves sufficiently far beyond R / Q, the two notions diverge wildly. After reviewing these results, we will discuss recent joint work with Clinton Conley, seeking to explain the difficulty in understanding definable cardinality beyond R / Q by showing that the aforementioned wild behavior occurs immediately thereafter. This will be a non-technical introduction to the subject, and should be accessible to anyone with an understanding of basic linear algebra and measure theory.

Date: Friday, August 30, 2013
Time: 4:30 pm
Location: Wean 7500
Submitted by:  Schimmerling