{"title":"H-D Ebbinghaus","description":null,"products":[{"product_id":"mathematical-logic-book-h-d-ebbinghaus-9780387942582","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":"GB \/ NEW \/ GARDNERS","offer_id":51157037941009,"sku":"NGR9780387942582","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51452214247697,"sku":"GOR005091318","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":51694668677393,"sku":"CIN0387942580G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52133915590929,"sku":"NLS9780387942582","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387942580.jpg?v=1751071695"},{"product_id":"zahlen-book-h-d-ebbinghaus-9783540126669","title":"Zahlen","description":"A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of number- told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi- cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec- tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52661428617489,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52661430059281,"sku":"NLS9783540126669","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540126669.jpg?v=1762267418"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-h-d-ebbinghaus.oembed","provider":"World of Books ","version":"1.0","type":"link"}