Logic Seminar: Some Computabiity-theoretic Aspects of Partition Regularity over Algebraic Structures, by Gabriela Laboska
October 1, 2024
4:00 PM - 4:50 PM
Gabriela Laboska (University of Chicago): Some Computabiity-theoretic Aspects of Partition Regularity over Algebraic Structures
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. We analyze some of these combinatorial
results from a computability-theoretic point of view, starting with
a theorem by Straus used directly or as a motivation to many of the
previous results on the subject.
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Date posted
Oct 7, 2024
Date updated
Oct 7, 2024
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