Nonstandard natural numbers in Ramsey theory

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Speaker: 
Mauro Di Nasso
Institution: 
University of Pisa
Time: 
Wed, 05/30/2018 - 4:00pm
Location: 
RH 440R

In  Ramsey  Theory, ultrafilters often play an instrumental role.
By using nonstandard models of the integers, one can replace those
third-order objects (ultrafilters are families of subsets) by simple
points.

In this talk we present a nonstandard technique that is grounded
on the above observation, and show its use in proving some new results
in Ramsey Theory of Diophantine equations.