Oberseminar "Mathematische Logik" - Nicholas Pischke

On the surface, a wide range of areas from mathematics, ranging for example from the duality theory of Banach spaces to the theory of probability measures, require the use of proof-theoretically strong principles to already develop the respectively most basic notions. Contrary to these theoretical limitations, we present recent approaches for extending the program of proof mining to some of these areas. This relies on the construction of systems that use intensional methods to deal with the high quantifier complexity of the predicates defining the objects of concern. These systems are then amenable to proof mining metatheorems, elucidating the extend of the phenomenon of so-called proof-theoretic tameness of modern mathematics as originally highlighted by Ulrich Kohlenbach, i.e. they show that also these areas adhere to the empirical fact that most respective proofs, although in principle being subject to well-known Goedelian phenomena, nevertheless "seem to be tame in the sense of allowing for the extraction of bounds of rather low complexity".