A Constructive Interpretation of Ramsey's Theorem via the Product of   Selection Functions
  We use G\"{o}del's Dialectica interpretation to produce a computational version of the well known proof of Ramsey's theorem by Erd\H{o}s and Rado. Our proof makes use of the product of selection functions, which forms an intuitive alternative to Spector's bar recursion when interpreting proofs in analysis. This case study is another instance of the application of proof theoretic techniques in mathematics. 
Paulo Oliva and Thomas Powell
math.LO cs.LO