The Measure Problem and Large Cardinals

Venue: The event will take place online through the ZOOM platform. To get the access codes please contact the secretary office (phd.maths [at] unitn.it)
Time: 2.30 p.m.

Gabrele Buriola - PhD in Mathematics, University of Trento

Abstract:The discovery of cardinals at the end of the nineteenth century, by Cantor, is one of the greatest milestones in modern mathematics. Almost all mathematicians have heard about their properties, which at first glance may seem paradoxical, and the issues they are involved in, such as the Continuum Hypothesis. Moreover, some further results highlighted the connections between measure theory and large cardinals. In this seminar we will present one of these results. More precisely, we will show a theorem, proved by Ulam, which relates the existence of a nontrivial σ-complete probabilistic measure over a set with the existence of some large cardinals, namely inaccessible and weakly inaccessible cardinals. The theorem has also a corollary concerning the existence of an extension of Lebesque measure to all subsets of ℝ in ZFC.

Contact person: Stefano Baratella

The seminar corresponds to the final exam of Set Theory, a planned course within Buriola Gabriele’s  first year PHD study programme