VIP systems in partial semigroups (Q5948968)

The notion of a VIP system in an Abelian group was introduced by \textit{V. Bergelson, H. Furstenberg} and \textit{R. McCutcheon} [in Ergodic Theory Dyn. Syst. 16, No. 5, 963-974 (1996; Zbl 0958.28013)] in order to extend some classic combinatorial results (like van der Waerden's theorem on arithmetic progressions) to the polynomial case.NEWLINENEWLINENEWLINEIn the article under review, Hindman and McCutcheon extend the notion of a VIP system to commutative partial semigroups and obtain an analogue of Furstenberg's central sets theorem for these systems. As an application, the authors deduce several Ramsey type theoretic facts.