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SUMMARY:Gabriela Laboska (Northwestern University)
DTSTART:20260430T180000Z
DTEND:20260430T190000Z
DTSTAMP:20260513T195517Z
UID:OLS/207
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/207/">So
 me Computabiity-theoretic and Reverse-mathematical Aspects of Partition Re
 gularity over Algebraic Structures</a>\nby Gabriela Laboska (Northwestern 
 University) as part of Online logic seminar\n\n\nAbstract\nAn inhomogeneou
 s system of linear equations over a ring $R$ is partition\nregular if for 
 any finite coloring of $R$\, the system has a monochromatic\nsolution. In 
 1933\, Rado showed that an inhomogeneous system is partition\nregular over
  $\\mathbb{Z}$ if and only if it has a constant solution.\nFollowing a sim
 ilar approach\, Byszewski and Krawczyk showed that the\nresult holds over 
 any integral domain. In 2020\, Leader and Russell\ngeneralized this over a
 ny commutative ring $R$\, with a more direct\nproof than what was previous
 ly used. In this talk\, we analyze a theorem by Straus from a computabilit
 y-theoretic and reverse-mathematical point of view. Straus' theorem has be
 en\nused directly or as a motivation to many of the results in this area.\
 n
LOCATION:https://researchseminars.org/talk/OLS/207/
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