A Multidimensional Central Sets Theorem
Mathias Beiglb\"ock
TL;DR
This paper presents a unified extension of the Central Sets Theorem and Ramsey's Theorem, broadening their applicability to general commutative semigroups in partition Ramsey theory.
Contribution
It introduces a multidimensional version that combines the strengths of both theorems, advancing the theoretical framework of partition Ramsey theory.
Findings
Unified extension of Central Sets and Ramsey's Theorem
Applicable to general commutative semigroups
Enhances understanding of partition Ramsey theory
Abstract
The Theorems of Hindman and van der Waerden belong to the classical theorems of partition Ramsey Theory. The Central Sets Theorem is a strong simultaneous extension of both theorems that applies to general commutative semigroups. We give a common extension of the Central Sets Theorem and Ramsey's Theorem.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory