By Goedel's inclompeteness theorem there is no completeaxiomatization of mathematics, not even of first orderarithmetic. This leads naturally to the project of... » 

By Goedel's inclompeteness theorem there is no completeaxiomatization of mathematics, not even of first orderarithmetic. This leads naturally to the project of investigating the family of, inevitably incomplete, arithmetical theories. In this book we present some of the results obtained in pursuing this aim. «