arXiv subjects

Zu Yao Teoh

Publications and source records attributed to Zu Yao Teoh.

4 recordsLinked to original sources

arXiv2020

Structural Considerations of Ramsey Algebras

Ramsey algebras is an attempt to investigate Ramsey spaces generated by algebras in a purely combinatorial fashion. Previous studies have focused on the basic properties of Ramsey algebras and the study of a few specific examples. In this article, we study the properties of Ramsey algebras from a structural point of view. For instance, we will see that isomorphic algebras have the same Ramsey algebraic properties, but elementarily equivalent algebras need not be so, as expected. Answer to a long-standing question about the Cartesian products of Ramsey algebras is also given.

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arXiv2017

A Ramsey Algebraic Study of Matrices

The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying manner. For the class of spaces generated by algebras, Carlson had suggested that one should attempt a purely combinatorial approach to the study. This approach was later formulated and named Ramsey algebra. In this paper, we continue to look at heterogeneous Ramsey algebras, mainly characterizing various Ramsey algebras involving matrices.

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arXiv2017

Ramsey Orderly Algebras as a New Approach to Ramsey Algebras

Ramsey algebras are algebras that induce Ramsey spaces, which are generalizations of the Ellentuck space and Milliken's space. Previous work suggests a possible local version of Ramsey algebras induced by infinite sequences. Hence, we introduce a new structure called orderly algebra. Under our canonical setup, an algebra is Ramsey if and only if every of its induced orderly algebra is Ramsey. In this paper, we present justifications for this novel notion as a sound approach for further study on Ramsey algebras.

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arXiv2017

Heterogeneous Ramsey Algebras and Classification of Ramsey Vector Spaces

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.

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