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thông tin biểu ghi
ISBN 9783319972978
DDC 511.3
Tác giả CN Kossak, Roman
Nhan đề Mathematical logic : on numbers, sets, structures, and symmetry / Roman author Kossak
Thông tin xuất bản Cham, Switzerland : Springer, 2018
Mô tả vật lý 188 pages. : illustrations
Tùng thư Springer graduate texts in philosophy, v. 3.
Tóm tắt This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Thuật ngữ chủ đề Mathematics
Thuật ngữ chủ đề Logic
Thuật ngữ chủ đề Logic, Symbolic and mathematical
Thuật ngữ chủ đề Mathematics-Philosophy
Từ khóa tự do Computer science
Khoa Khoa Cơ bản
Địa chỉ Thư Viện Đại học Nguyễn Tất Thành
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100 |aKossak, Roman|d1953-
245 |aMathematical logic : |bon numbers, sets, structures, and symmetry / |cRoman author Kossak
260 |aCham, Switzerland : |bSpringer, |c2018
300 |a188 pages. : |billustrations
490 |aSpringer graduate texts in philosophy, v. 3.
504 |aIncludes bibliographical references (pages 185-186) and index.
520 |aThis book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
541 |aSpringer
650 |aMathematics
650 |aLogic
650 |aLogic, Symbolic and mathematical
650 |aMathematics|xPhilosophy
653 |aComputer science
690 |aKhoa Cơ bản
852 |aThư Viện Đại học Nguyễn Tất Thành
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