Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 14 February 2018, 17:00 hrs Room: S17#0406, 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 nonempty. If X is assumed to be effectively closed then this is the wellknown axiom WWKL0. 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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