Dynamical characterization of C-sets and its application

TL;DR

This paper establishes a link between algebraic properties of natural numbers and dynamical sets, providing a new characterization of C-sets and demonstrating their applicability to solving Rado systems.

Contribution

It introduces a dynamical characterization of C-sets and applies this to prove Rado systems are solvable within C-sets.

Findings

Dynamical characterization of C-sets established

Rado systems are solvable in C-sets

Connection between algebraic and dynamical properties of sets

Abstract

In this paper, we set up a general correspondence between the algebra properties of $\bN$ and the sets defined by dynamical properties. In particular, we obtain a dynamical characterization of C-sets, where C-sets are the sets satisfying the strong Central Sets Theorem. As an application, we show that Rado systems are solvable in C-sets.