The Limits of Mathematics---Third Version

Abstract

This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are further reduced. This is done by inventing a more complicated version of lisp in which the parentheses associating defined functions with their arguments can be omitted. This is the third and last version of my course notes. It is not clear to me which is to be preferred, so all three have been made available for comment.