Mathematical Logic
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Mathematical Logic
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Author : Stephen Cole Kleene
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Mathematical Logic written by Stephen Cole Kleene and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
Mathematical Logic
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Author : Roman Kossak
language : en
Publisher: Springer Nature
Release Date : 2024-04-18
Mathematical Logic written by Roman Kossak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. 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 usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and 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.
Mathematical Logic
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Author : Joseph R. Shoenfield
language : en
Publisher: CRC Press
Release Date : 2018-05-02
Mathematical Logic written by Joseph R. Shoenfield and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-02 with Mathematics categories.
This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.
Mathematical Logic
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Author : Willard Van Orman Quine
language : en
Publisher: Harvard University Press
Release Date : 1981
Mathematical Logic written by Willard Van Orman Quine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
W. V. Quine’s systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition. This revised edition, in which the minor inconsistencies observed since its first publication have been eliminated, will be welcomed by all students and teachers in mathematics and philosophy who are seriously concerned with modern logic. Max Black, in Mind, has said of this book, “It will serve the purpose of inculcating, by precept and example, standards of clarity and precision which are, even in formal logic, more often pursued than achieved.”
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer
Release Date : 2014-11-07
Mathematical Logic written by Wei Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Mathematical Logic
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Author : Petio P. Petkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Logic written by Petio P. Petkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Heyting'88 Summer School and Conference on Mathematical Logic, held September 13 - 23, 1988 in Chaika, Bulgaria, was honourably dedicated to Arend Heyting's 90th anniversary. It was organized by Sofia University "Kliment Ohridski" on the occasion of its centenary and by the Bulgarian Academy of Sciences, with sponsorship of the Association for Symbolic Logic. The Meeting gathered some 115 participants from 19 countries. The present volume consists of invited and selected papers. Included are all the invited lectures submitted for publication and the 14 selected contributions, chosen out of 56 submissions by the Selection Committee. The selection was made on the basis of reports of PC members, an average of 4 per sLlbmission. All the papers are concentrated on the topics of the Meeting: Recursion Theory, Modal and Non-classical Logics, Intuitionism and Constructivism, Related Applications to Computer and Other Sciences, Life and Work of Arend Heyting. I am pleased to thank all persons and institutions that contributed to the success of the Meeting: sponsors, Programme Committee members and additional referees, the members of the Organizing Committee, our secretaries K. Lozanova and L. Nikolova, as well as K. Angelov, V. Bozhichkova, A. Ditchev, D. Dobrev, N. Dimitrov, R. Draganova, G. Gargov, N. Georgieva, M. Janchev, P. Marinov, S. Nikolova, S. Radev, I. Soskov, A. Soskova and v. Sotirov, who helped in the organization, Plenum Press and at last but not least all participants in the Meeting and contributors to this volume
Introduction To Mathematical Logic Extended Edition
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Author : Michal Walicki
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-08-12
Introduction To Mathematical Logic Extended Edition written by Michal Walicki and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-12 with Mathematics categories.
This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.
Introduction To Mathematical Logic
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Author : Jayant Ramaswamy
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Introduction To Mathematical Logic written by Jayant Ramaswamy and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Introduction to Mathematical Logic" is tailored for undergraduate students seeking a comprehensive introduction to this essential field of mathematics. We provide an accessible yet rigorous exploration of the principles, methods, and applications of mathematical logic. From the foundations of propositional and predicate logic to advanced topics like Gödel's incompleteness theorems and computability theory, we cover a broad range of concepts central to the study of logic. Through clear explanations, illustrative examples, and carefully crafted exercises, students will develop a deep understanding of logical reasoning, formal proof techniques, and the structure of mathematical arguments. Moreover, we emphasize the interdisciplinary nature of mathematical logic, showcasing its relevance in mathematics, philosophy, computer science, and beyond. Real-world applications of logical reasoning are woven throughout the text, demonstrating how logical principles underpin various fields of study, from algorithm design and formal verification to philosophical analysis and linguistic theory. Whether you're a mathematics major, a philosophy student, or pursuing studies in computer science, this book equips you with the tools and insights necessary to navigate the complexities of mathematical logic with confidence. With its blend of theory and application, this text serves as an invaluable resource for undergraduate students embarking on their journey into the realm of mathematical logic.
Mathematical Logic
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Author : H.-D. Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Mathematical Logic written by H.-D. Ebbinghaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Mathematical Logic
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer Nature
Release Date : 2021-05-28
Mathematical Logic written by Heinz-Dieter Ebbinghaus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Mathematics categories.
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.