Книга “Логика математики” автора Зофии Адамович является подробным, доступным и строгим представлением центральных теорем математической логики . . . идеально подходит для продвинутых студентов математики, компьютерных наук и логики. Логика математики сочетает в себе полноценный вводный курс по математической логике и теории моделей с рядом специально отобранных, более продвинутых теорем. Используя строгий математический подход, это единственная книга, содержащая полные и точные доказательства всех этих важных теорем: * теоремы Гёделя о полноте и неполноте; * независимость теоремы Гудштейна от арифметики Пеано; * теорема Тарского о реальных замкнутых полях; * теорема Матиясевича о диофантовых формулах. Книга также содержит полное освещение теоретических тем, таких как определенность, компактность, ультрапродукты, реализация и отсутствие типов. В ней также представлены четкие и лаконичные объяснения всех ключевых понятий, от булевых алгебр до .
Of Mathematics covers the central theorems in mathematical logic in complete detail. It combines a thorough introductory course with specially selected advanced theorems and covers Gödel’s theorems, Goodstein’s independence, Tarksi’s real field theorem and many other important results.
Электронная Книга «Logic of Mathematics - Zofia Adamowicz» написана автором Zofia Adamowicz в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9781118030790
Описание книги от Zofia Adamowicz
A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic 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: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints 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. 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. 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. 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.
