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SUMMARY:Canonical Ramsey Theory and The Idea of a Foundation for Mathemati
 cs - Natasha Dobrinen (University of Denver) and Juliette Kennedy (Univers
 ity of Helsinki)
DTSTART:20151118T173000Z
DTEND:20151118T183000Z
UID:TALK62575@talks.cam.ac.uk
CONTACT:34012
DESCRIPTION:Idea of a Foundation for Mathematics: I will review some of th
 e history of foundations\, starting from Frege through to the Hilbert Prog
 ram\, leading up to the Incompleteness Theorems of 1931 due to Kurt Gödel
 .  I will discuss my own approach to foundations at the end\, a "local fou
 ndations" point of view.\n\nCanonical Ramsey Theory:  The infinite Ramsey'
 s Theorem states that whenever all\npairs of natural numbers are colored b
 y finitely many colors\, there is\nan infinite set on which all pairs have
  the same color.  When one\nwishes to use infinitely many colors\, in othe
 r words an equivalence\nrelation\, it is not always possible to find an in
 finite set on which\nall pairs have the same color.  However\, a breakthro
 ugh of Erdos and\nRado show that there is always an infinite set on which 
 the\nequivalence relation is one of only four canonical types.  We will\nd
 iscuss this canonical Ramsey theorem and some of our related work\nfinding
  canonical equivalence relations on other classes of finite\nstructures wi
 th the Ramsey property\, as well as applications in set\ntheory.
LOCATION:Mill Lane Lecture Room 6
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