Some Computabiity-theoretic and Reverse-mathematical Aspects of Partition Regularity over Algebraic Structures

Abstract: An inhomogeneous system of linear equations over a ring $R$ is partition regular if for any finite coloring of $R$, the system has a monochromatic solution. In 1933, Rado showed that an inhomogeneous system is partition regular over $\mathbb{Z}$ if and only if it has a constant solution. Following a similar approach, Byszewski and Krawczyk showed that the result holds over any integral domain. In 2020, Leader and Russell generalized this over any commutative ring $R$, with a more direct proof than what was previously used. In this talk, we analyze a theorem by Straus from a computability-theoretic and reverse-mathematical point of view. Straus' theorem has been used directly or as a motivation to many of the results in this area.

discrete mathematicscombinatoricslogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic