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Graduate Seminar
William Gunther Carnegie Melllon University Title: Lambda Calculus and the Decision Problem Abstract: In 1928, Alonzo Church formalized the $lambda$calculus, which was an attempt at providing a foundation for mathematics. At the heart of this system was the idea of function abstraction and application. In this talk, I will outline the early history and motivation for $lambda$calculus, especially in recursion theory. I will discuss the basic syntax and the primary rule: $beta$reduction. Then I will show how one would represent certain structures and control statements (numbers, pairs, ifthenelse statements, etc) in this system. This will lead into some theorems about fixed points which will allow us to have some fun and (if there is time) to supply a negative answer to Hilbert's Entscheidungsproblem: is there an effective way to give a yes or no answer to any mathematical statement. Date: Tuesday, November 9, 2010 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Daniel Spector 