# Higher-order Reverse Mathematics: Where existence meets computation via infinitesimals.

## Sam Sanders

### Department of Mathematics, Ghent University

Classically, the existence of an object tells us very little about how to construct said object.

We consider a nonstandard version of Ulrich Kohlenbach’s higher-order Reverse Mathematics

in which there is a very elegant and direct correspondence between, on one hand, the existence

of a functional computing an object and, on the other hand, the classical existence of this object

with the same standard and nonstandard properties. We discuss how these results -potentially-

contribute to the programs of finitistic and predicativist mathematics.

Sam Sanders finished his PhD in 2010 at Ghent University, under the supervision of Andreas Weiermann and Chris Impens, and now holds a postdoctoral position there. He studies analysis and the foundations of mathematics, doing work in reverse mathematics using nonstandard analysis, proof theory, and computability theory.