Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic

Henry Towsner

Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic

Logic 2009-06-23 v1 Combinatorics

Authors: Henry Towsner

Abstract

Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.

Keywords

ultrafilter fundamental theorem general mathematical theorems and proofs

Cite

@article{arxiv.0906.3882,
  title  = {Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic},
  author = {Henry Towsner},
  journal= {arXiv preprint arXiv:0906.3882},
  year   = {2009}
}