Additive and multiplicative structure of c${}^{\star }$-sets

Abstract

It is known that for an IP${}^{\star }$ set $A$ in $\mathbb{N}$ and a sequence $<x_n{>}_{n=1}^{\infty }$ there exists a sum subsystem $<y_n{>}_{n=1}^{\infty }$ of $<x_n{>}_{n=1}^{\infty }$ such that $FS(<y_n{>}_{n=1}^{\infty })\cup FP(<y_n{>}_{n=1}^{\infty })\subseteq A$. Similar types of results also have been proved for central* sets where the sequences have been taken from the class of minimal sequences. In this present work we will prove some analogues results for C${}^{\star }$-sets for a more general class of sequences.

final version

References in corpus (1)

• Dynamical characterization of C-sets and its application