THE WEIHRAUCH LATTICE AT THE LEVEL OF Π11-CA0: THE CANTOR-BENDIXSON THEOREM

Abstract

This paper continues the program connecting reverse mathematics and computable analysis via the framework ofWeihrauch reducibility. In particular, we consider problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor-Bendixson theorem, and various problems arising from them. In the framework of reverse mathematics, these theorems are equivalent, respectively, to ATR0 and Π11 -CA0, the two strongest subsystems of second order arithmetic among the so-called big five. As far as we know, this is the first systematic study of problems at the level of Π11 -CA0 in the Weihrauch lattice.We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough