A new version of algorithmic information theory

Algorithmic information theory may be viewed as the result of adding the idea of program-size complexity to recursive function theory. The main application of algorithmic information theory is its informationtheoretic incompleteness theorems. This theory is concerned with the size of programs, but up to now these have never been programs that one could actually program out and run on interesting examples. I have now figured out how to actually program the algorithms in the proofs of the all the key information-theoretic incompleteness theorems in algorithmic information theory. I have published this material electronically in a series of detailed reports [1,2,3,4]