On \(\text{IP}^*\) sets and central sets. (English) Zbl 0820.05061

Summary: \(\text{IP}^*\) sets and central sets are subsets of \(\mathbb{N}\) which are known to have rich combinatorial structure. We establish here that this structure is significantly richer than was previously known. We also establish that multiplicatively central sets have rich additive structure. The relationship among \(\text{IP}^*\) sets, central sets, and corresponding dynamical notions are also investigated.


05D10 Ramsey theory
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