A Study Of Some Generalized Central Sets Theorem Along Phulara's Way

TL;DR

This paper extends the Central Sets Theorem along Dev Phulara's approach, providing generalized versions and applications in Ramsey theory, building on prior foundational work by Hindman, Leader, De, and Strauss.

Contribution

It introduces new generalized versions of the Central Sets Theorem along Dev Phulara's method, expanding its scope and applications.

Findings

Multiple generalized versions of the Central Sets Theorem are established.

The paper demonstrates Ramsey theoretic applications of these generalized theorems.

It shows the theorem's validity for sequences of central sets instead of single sets.

Abstract

The Central Sets Theorem near zero was originally proved by Hindman and Leader. Later a version of Central Sets Theorem was proved by De, Hindman and Strauss known to be the stronger Central Sets Theorem. Subsequently many other versions of Central Sets Theorem came, among which Dev Phulara proved the theorem for a sequence of central sets instead of taking one set. In this paper, we provide various general versions of the theorem along Dev Phulara's way with some Ramsey theoretic applications.