Nonstandard analysis and partition properties of the natural numbers

Many theorems in combinatorial number theory are of the following form: If P is a property that holds for the set of all natural numbers, and A, B are disjoint subsets whose union is the set of all natural numbers, then either A or B has the property P. For instance, either A or B must be infinite, which is the Pigeonhole Principle. We present some recent work on such properties using methods from nonstandard analysis.

Ryan Utke