This is an up-to-date exposition of Gödel's theory on the incompleteness of functional calculi which include ordinary arithmetic. In spite of the author's modest remarks, no strictly comparable work exists, at least to the reviewer's knowledge. There are indeed other books which contain chapters on Gödel's works, but none is entirely focussed on it like the present monograph. Apart from that, the author makes an original contribution to the subject by providing a unified treatment of the various methods of approach which have been put forward.
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