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CATEGORIES:Emmy Noether Society
SUMMARY:Canonical Ramsey Theory and The Idea of a Foundati
on for Mathematics - Natasha Dobrinen (University
of Denver) and Juliette Kennedy (University of Hel
sinki)
DTSTART;TZID=Europe/London:20151118T173000
DTEND;TZID=Europe/London:20151118T183000
UID:TALK62575AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62575
DESCRIPTION:Idea of a Foundation for Mathematics: I will revie
w some of the history of foundations\, starting fr
om Frege through to the Hilbert Program\, leading
up to the Incompleteness Theorems of 1931 due to K
urt GĂ¶del. I will discuss my own approach to foun
dations at the end\, a "local foundations" point o
f view.\n\nCanonical Ramsey Theory: The infinite
Ramsey's Theorem states that whenever all\npairs o
f natural numbers are colored by finitely many col
ors\, there is\nan infinite set on which all pairs
have the same color. When one\nwishes to use inf
initely many colors\, in other words an equivalenc
e\nrelation\, it is not always possible to find an
infinite set on which\nall pairs have the same co
lor. However\, a breakthrough of Erdos and\nRado
show that there is always an infinite set on which
the\nequivalence relation is one of only four can
onical types. We will\ndiscuss this canonical Ram
sey theorem and some of our related work\nfinding
canonical equivalence relations on other classes o
f finite\nstructures with the Ramsey property\, as
well as applications in set\ntheory.
LOCATION:Mill Lane Lecture Room 6
CONTACT:
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