Call a program "elegant" if no smaller program has the same output. I.e., a LISP S-expression is defined to be elegant if no smaller S-expression has the same value. It is impossible to prove that any particular large program is elegant.

The necessary and sufficient condition for the existence of a uniquely decodable code for a given set of codeword lengths. Relevant for binary trees, Chaitin's constant.

Chaitin compares and contrasts Gödel's, Turing's and his own work in a straight-forward manner using Lisp.