Geodesic
D sets and IP rich sets in $\mathbb {Z}$
Randall McCutcheon 1   ; Jee Zhou 1
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
Fundamenta Mathematicae, Tome 233 (2016) no. 1, pp. 71-82 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm950-11-2015
Keywords: combinatorial characterizations mathrm rich sets mathrm sets remain mathrm removal set zero upper banach density sets members idempotent ultrafilters whose members have positive upper banach density mathbb family mathrm rich sets strictly contains family sets

Randall McCutcheon  1   ; Jee Zhou  1

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A. 
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Randall McCutcheon; Jee Zhou. D sets and IP rich sets in $\mathbb {Z}$. Fundamenta Mathematicae, Tome 233 (2016) no. 1, pp. 71-82. doi: 10.4064/fm950-11-2015

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