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UID:20251218T232211EST-6709X4Nssl@132.216.98.100
DTSTAMP:20251219T042211Z
DESCRIPTION:Finite versus infinite\, an intricate shift\n\nThe Borel chroma
 tic number - introduced by Kechris\, Solecki\, and Todorcevic (1999) - gen
 eralizes the chromatic number on finite graphs to definable graphs on topo
 logical spaces. While the G0 dichotomy states that there exists a minimal 
 graph with uncountable Borel chromatic number\, it turns out that characte
 rizing when a graph has infinite Borel chromatic number is far more intric
 ate. Even in the case of graphs generated by a single function\, our under
 standing is actually very poor. The Shift Graph on the space of infinite s
 ubsets of natural numbers is generated by the function that removes the mi
 nimum element. It is acyclic but has infinite Borel chromatic number. In 1
 999\, Kechris\, Solecki\, and Todorcevic asked whether the Shift Graph is 
 minimal among the graphs generated by a single Borel function that have in
 finite Borel chromatic number. I will explain why the answer is negative u
 sing a representation theorem for Σ12 sets due to Marcone.\n
DTSTART:20180925T183000Z
DTEND:20180925T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Yann Pequignot\, 9IÖÆ×÷³§Ãâ·Ñ
URL:/mathstat/channels/event/yann-pequignot-mcgill-289
 922
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