  This is yet another version of the course notes in chao-dyn/9407003. Here we
use m-expressions more aggressively to further reduce the constants in our
information-theoretic incompleteness theorems. Our main theorems are: 1) an
N-bit formal axiomatic system cannot enable one to exhibit any specific object
with program-size complexity greater than N+c, 2) an N-bit formal axiomatic
system cannot enable one to determine more than N+c' scattered bits of the
halting probability Omega. In chao-dyn/9407003, c = 2359 bits and c' = 7581
bits. In chao-dyn/9407005, c = 1127 bits and c' = 3689 bits. In
chao-dyn/9407006, c = 994 bits and c' = 3192 bits. And in this version, c = 735
bits and c' = 2933 bits.
