Heterogeneous Ramsey Algebras and Classification of Ramsey Vector Spaces

TL;DR

This paper extends the concept of Ramsey algebras to heterogeneous algebras and explores their properties, particularly focusing on vector spaces, to deepen understanding of their combinatorial and algebraic structures.

Contribution

It introduces the notion of Ramsey algebras for heterogeneous algebras and investigates their properties, especially in the context of vector spaces.

Findings

Basic results for heterogeneous Ramsey algebras are established.

Ramsey-algebraic properties of vector spaces are analyzed.

The study broadens the scope of Ramsey algebra theory to new algebraic structures.

Abstract

Carlson introduced the notion of a Ramsey space as a generalization to the Ellentuck space. When a Ramsey space is induced by an algebra, Carlson suggested a study of its purely combinatorial version now called Ramsey algebra. Some basic results for homogeneous algebras have been obtained. In this paper, we introduce the notion of a Ramsey algebra for heterogeneous algebras and derive some basic results. Then, we study the Ramsey-algebraic properties of vector spaces.