Partition regularity over algebraic structures is a topic in Ramsey theory that has been extensively researched by combinatorialists. 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 thesis focuses on a 1975 theorem by Straus, which has played a significant role in many of the results in this field.

We show that Straus’ theorem does not hold computably, and we investigate different cases of the theorem. For the simplest case n = 1, we show that the best possible computability-theoretic bound for this problem are the PA degrees. We show something similar for the case n > 1, under one additional condition.

Since the PA degrees already have implications for the reverse mathematics of the theorem, we show that several cases of the theorem are equivalent to WKL₀ over RCA₀, as well as the fact that WKL₀ implies the full Straus’ theorem over RCA₀.