Abstract

V. Bergelson and N. Hindman proved that if 〈xn〉n=1∞ is a sequence in (N,+), then for any IP⁎ set A there exists a sum subsystem 〈yn〉n=1∞ of 〈xn〉n=1∞ with the property that FS(〈yn〉n=1∞)∪FP(〈yn〉n=1∞)⊆A. While extending this combined structure, we obtain that a stronger result holds for dynamical IP⁎ sets. But for any IP⁎ set, it is unknown.

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