Algorithmic information theory - Chaitin, Gregory J. (Cambridge University Press, 2004)
The inventor of algorithmic information theory, presents in this book the strongest possible version of Godel's incompleteness theorem, using an information theoretic approach based on the size of computer programs." This slim but highly original (and frequently lively) monograph brings to mind the (related) work of Godel and of Turing; it is methodologically/stylistically idiosyncratic, and addressed to the clarification of some deeply fundamental issues"the nature of randomness and the limitations of the axiomatic method."