Wang Wei: Combinatorics and Probability in First and Second Order Arithmetic

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 14 February 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Wang Wei

Title: Combinatorics and Probability in First and Second Order Arithmetic

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
Recent years see emergence of connections between the reverse mathematics
of Ramsey theory and computable measure theory or algorithmic randomness.
Here we consider two simple propositions in measure theory which have
interesting connections to the reverse mathematics of Ramsey theory. The
first is that every set X in Cantor space of positive Lebesgue measure is
non-empty. If X is assumed to be effectively closed then this is the
well-known axiom WWKL-0. However, if X is allowed to be a
little wilder and the proposition is twisted a bit, then it could help in
understanding the first order theory of some Ramseyan theorems. The second
is that every set X in Cantor space of positive measure has a perfect
subset. This proposition is somehow related to a tree version of Ramsey's
theorem. But unlike the first one, it is not familiar to people either in
algorithmic randomness or reverse mathematics.

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