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Constructive Reverse Mathematics

Dr Hannes Diener, University of Siegen, Germany
Tuesday, 16 August 2011, 16h00, M 111 (Seminar Room)

Working in constructive mathematics, that is mathematics with intuitionistic logic, many classically valid statements, such as the uniform continuity theorem, become independent of the underlying framework; that is neither the statement nor its antithesis is provable by purely constructive methods. Nevertheless, one can often show the equivalence of such statements. The systematic endeavour to identify classes of statements that are equivalent over intuitionistic logic has become known as "constructive reverse mathematics" (CRM). In this talk we will give a brief introduction to constructive mathematics in general, present a basic overview of CRM, and highlight some of the intricacies and open questions. Furthermore, we will compare CRM to similar endeavours such as "classical" reverse mathematics (a la Simpson) and the Weihrauch lattice.

Measurability in Modules

Charlotte Kestner, University of Leeds, UK
Thursday, 28 April 2011, 16h00, M 214

In this talk I will start with an introduction to the model theory of modules. I will then introduce the notion of a measurable theory, discuss measurability in modules, with specific examples in abelian groups.