Mathematical Logic

What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe­ matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first—order logic. Our first goal is Godel's completeness theorem, which shows that the con­ sequence relation coincides with formal pr...