English

Nonstandard proof of combined sum and product structure in IP$^{*}$ sets

Combinatorics 2021-10-19 v1

Abstract

V. Bergelson and N. Hindman proved that IPIP^{*} sets contain all possible finite sum and product of a sum subsystem of any sequence in N\mathbb{N}. In this article, we will prove this result using Nonstandard analysis.

Keywords

Cite

@article{arxiv.2110.09285,
  title  = {Nonstandard proof of combined sum and product structure in IP$^{*}$ sets},
  author = {Sayan Goswami},
  journal= {arXiv preprint arXiv:2110.09285},
  year   = {2021}
}