D sets and IP rich sets in $\mathbb {Z}$
Volume 233 / 2016
Fundamenta Mathematicae 233 (2016), 71-82
MSC: Primary 22A15; Secondary 05D10.
DOI: 10.4064/fm950-11-2015
Published online: 25 November 2015
Abstract
We give combinatorial characterizations of $\mathrm {IP}$ rich sets ($\mathrm {IP}$ sets that remain $\mathrm {IP}$ upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultrafilters, all of whose members have positive upper Banach density) in $\mathbb Z$. We then show that the family of $\mathrm {IP}$ rich sets strictly contains the family of D sets.
