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STRUCTURAL CONSIDERATIONS OF RAMSEY ALGEBRAS

Part of: Set theory Extremal combinatorics General logic

Published online by Cambridge University Press:  29 October 2021

ZU YAO TEOH Open the ORCID record for ZU YAO TEOH [Opens in a new window]
ZU YAO TEOH*
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES UNIVERSITI SAINS MALAYSIA11800 USM, MALAYSIA
*
E-mail:[email protected]
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Abstract

Ramsey algebras are 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 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. We also answer an open question about Cartesian products of Ramsey algebras.

Keywords

Ramsey algebraHindman’s theoremRamsey spaceEllentuck space

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 05D10: Ramsey theory 03B80: Other applications of logic
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 4 , December 2022 , pp. 1677 - 1692
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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