ON THE EFFECTIVENESS OF PARTITION REGULARITY OVER ALGEBRAIC STRUCTURES

Abstract Partition regularity over algebraic structures is a topic in Ramsey theory that has been extensively researched by combinatorialists [2, 3, 5, 15]. Motivated by recent work in this area, we investigate the computability-theoretic and reverse-mathematical aspects of partition regularity over algebraic structures—an area that, to the best of our knowledge, has not been explored before. This article focuses on a 1975 theorem by Straus [25], which has played a significant role in many of the results in this field.