The papers gathered in this book were published over a period of
more than twenty years in widely scattered journals. They led to
the discovery of randomness in arithmetic which was presented in
the recently published monograph on "Algorithmic Information
Theory" by the author. There the strongest possible version of
Goedel's incompleteness theorem, using an information-theoretic
approach based on the size of computer programs, was discussed. The
present book is intended as a companion volume to the monograph and
it will serve as a stimulus for work on complexity, randomness and
unpredictability, in physics and biology as well as in
metamathematics.
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