|Los Angeles Math Circle|
5/27/2012 -- LAMC High School: Sentential Logic and the Compactness Theorem -- Bill Chen
We will first describe sentential logic, a language used to formalize certain kinds of assertions. Then, we will state and prove the compactness theorem of sentential logic, a result of fundamental importance that in some sense allows us to understand infinite collections of assertions by their finite subcollections. This will be used to prove a corollary about graph colorings.