{"product_id":"logic-of-mathematics-a-modern-course-of-classical-logic-hardback-9780471060260","title":"Logic of Mathematics; A Modern Course of Classical Logic (Hardback) 9780471060260","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLogic of Mathematics\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Modern Course of Classical Logic\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eZofia Adamowicz (Author), Pawel Zbierski (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780471060260, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 7 April 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e272 pages\u003cbr\u003e24 x 16.2 x 1.9 cm, 0.472 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eA thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic\u003cbr\u003e \u003cbr\u003e Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems:\u003cbr\u003e * Gödel's theorems of completeness and incompleteness\u003cbr\u003e * The independence of Goodstein's theorem from Peano arithmetic\u003cbr\u003e * Tarski's theorem on real closed fields\u003cbr\u003e * Matiyasevich's theorem on diophantine formulas\u003cbr\u003e \u003cbr\u003e Logic of Mathematics also features:\u003cbr\u003e * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types\u003cbr\u003e * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics\u003cbr\u003e * Carefully chosen exercises for each chapter, plus helpful solution hints\u003cbr\u003e \u003cbr\u003e At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms.\u003cbr\u003e \u003cbr\u003e Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more.\u003cbr\u003e \u003cbr\u003e Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems.\u003cbr\u003e \u003cbr\u003e With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePartial table of contents:\u003cbr\u003e \u003cbr\u003e MATHEMATICAL STRUCTURES AND THEIR THEORIES.\u003cbr\u003e \u003cbr\u003e Relational Systems.\u003cbr\u003e \u003cbr\u003e Boolean Algebras.\u003cbr\u003e \u003cbr\u003e Terms and Formulas.\u003cbr\u003e \u003cbr\u003e Substitution of Terms.\u003cbr\u003e \u003cbr\u003e Theorems and Proofs.\u003cbr\u003e \u003cbr\u003e Generalization Rule and Elimination of Constants.\u003cbr\u003e \u003cbr\u003e Peano Arithmetic.\u003cbr\u003e \u003cbr\u003e Ultraproducts.\u003cbr\u003e \u003cbr\u003e Supplementary Questions.\u003cbr\u003e \u003cbr\u003e SELECTED TOPICS.\u003cbr\u003e \u003cbr\u003e Total Functions.\u003cbr\u003e \u003cbr\u003e Incompleteness of Arithmetic.\u003cbr\u003e \u003cbr\u003e Tarski's Theorem.\u003cbr\u003e \u003cbr\u003e Matiyasevich's Theorem.\u003cbr\u003e \u003cbr\u003e Guide to Further Reading.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-Interscience","offers":[{"title":"Brand New","offer_id":52278196437272,"sku":"9780471060260","price":132.48,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780471060260.jpg?v=1781459377","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/logic-of-mathematics-a-modern-course-of-classical-logic-hardback-9780471060260","provider":"Freshly Printed Books","version":"1.0","type":"link"}