Solvability of Rado systems in D-sets
Dynamical Systems
2008-09-16 v1
Abstract
Rado's Theorem characterizes the systems of homogenous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado's Theorem.) We show that the same holds true for the larger class of -sets. Moreover we will see that the conclusion of Furstenberg's Central Sets Theorem is true for all sets in this class.
Cite
@article{arxiv.0809.2281,
title = {Solvability of Rado systems in D-sets},
author = {Mathias Beiglböck and Vitaly Bergelson and Tomasz Downarowicz and Alexander Fish},
journal= {arXiv preprint arXiv:0809.2281},
year = {2008}
}