Hindman's theorem and the hyperreals

Abstract: Hindman's theorem says that if the natural numbers are colored using finitely many colors, then there exists some color $c$ and some infinite $S\subseteq \mathbb N$ such that for every finite nonempty subset $\{n_1,\ldots,n_k\}$ of $S$, $n_1+\cdots+n_k$ is color $c$. We present a proof using hyperreal numbers, and a stronger version of the theorem involving hyperreal numbers. \\ Some of this material was previously published in 2024 in the Journal of Logic and Analysis.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)