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Weihrauch degrees for generalized Baire space

Presented by: 
L Galeotti Universiteit van Amsterdam
Date: 
Saturday 10th October 2015 - 11:00 to 11:55
Venue: 
INI Seminar Room 1
Abstract: 
The theory of Weihrauch degrees is about representing classical theorems of analysis in Baire space and comparing their strength (measured as the Weihrauch degree). In this talk, we are exploring a version of this theory for generalized Baire space. The first step in this generalization is that of finding a generalization of R on which we can prove a version of theorems from classical analysis. The first part of the talk will be devoted to the presentation of the construction of an extension of R on which we can prove a version of the Intermediate Value Theorem. In the second part of the talk we will be focusing on generalizing notions from computable analysis. Finally we will show how this new framework can be used to characterize the strength of the generalized version of the version of the Intermediate Value Theorem we presented in the first half of the talk.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons