Résume |
Many mathematical theorems can be viewed as problems: a statement of the form forall x in X (phi(x) implies exists y in Y psi(x,y)) is the problem of finding a suitable y starting from x.
Weihrauch reducibility allows to compare these (and many other) problems in a way that refines the analysis carried out in the framework of reverse mathematics. In the last 15 years this approach has been very fruitful, but until now it has almost exclusively dealt with theorems that reverse mathematics classifies at or below the level of ATR0.
We start the investigation of theorems at the level of Pi^1_1-comprehension by dealing with a classic result of descriptive set theory: the Cantor-Bendixson theorem, stating that every closed subset of a Polish space can be uniquely written as the disjoint union of a perfect set (the perfect kernel) and a countable set (the scattered part).
The talk will start with an introduction to Weihrauch reducibility and the Weihrauch lattice.
This is joint work with Vittorio Cipriani and Manlio Valenti |