A generalized central sets theorem in partial semigroups (Q2297056)

The main purpose of the paper is to establish the Central Sets Theorem for adequate commutative partial semigroups. While the original Central Sets Theorem deals with arbitrary sequences in \(\mathbb Z\), the author introduces the notion of adequate sequence and proves a version of the Central Sets Theorem for adequate sequences in adequate commutative partial semigroups. The paper also provides a sufficient condition for a set to satisfy the conclusion of the Central Sets Theorem proved by De, Hindman and Strauss [\textit{D. De} et al., Fundam. Math. 199, No. 2, 155--175 (2008; Zbl 1148.05052)].