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SUMMARY:On Ramsey-like theorems on the rationals and the Rado graph - Pete
 r Cholak (University of Notre Dame)
DTSTART:20220609T101500Z
DTEND:20220609T111500Z
UID:TALK174827@talks.cam.ac.uk
DESCRIPTION:Ramsey theorem implies for every 2-coloring of pairs of natura
 ls there is an infinite set H of naturals where all the pairs formed from 
 H have the same color.&nbsp\; We will explore how to extend this to the ra
 tionals\, the Rado graph and some other relational homogenous countable st
 ructures. One of the main tools used in these extensions is Milliken's tre
 e theorem and it&rsquo\;s recent modifications.&nbsp\; Our goal is to try 
 to understand the arithmetic complexity of the resulting &ldquo\;homogenou
 s&rdquo\; set or structure. I.e. if the colorings are computable is there 
 a &ldquo\;homogenous&rdquo\; structure within the arithmetical hierarchy a
 nd if so where.&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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