{"product_id":"mathematical-logic-book-heinz-dieter-ebbinghaus-9783030738419","title":"Mathematical Logic","description":"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 provability: By means of a calcu- lus consisting of simple formal inference rules, one can obtain all conse- quences of a given axiom system (and in particular, imitate all mathemat- ical proofs). A short digression into model theory will help us to analyze the expres- sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51060219642129,"sku":"","price":0.0,"currency_code":"USD","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51060223082769,"sku":"NIN9783030738419","price":49.99,"currency_code":"USD","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52430986248465,"sku":"NLS9783030738419","price":69.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3030738418.jpg?v=1750729149","url":"https:\/\/www.worldofbooks.com\/products\/mathematical-logic-book-heinz-dieter-ebbinghaus-9783030738419","provider":"World of Books ","version":"1.0","type":"link"}