Speaker: James Hunter (University of Wisconsin-Madison)
Title: Higher-Order Reverse Topology
Abstract:
Reverse Mathematics studies equivalences between logical axioms and
mathematical theorems. Traditional Reverse Mathematics is limited to
subsystems of second-order arithmetic, and thus can consider only those
mathematical theorems expressible in the language of second-order
arithmetic.
In a recent paper, Kohlenbach showed that Reverse Mathematics extends nicely
to higher-order theories, and examined certain higher-order statements in
mathematical analysis. The same techniques can be applied to statements
about topological spaces of size continuum, allowing for an examination
of statements more general than those studied by traditional Reverse
Mathematics.