## A Course in Mathematical Logic

**Author**: Yu.I. Manin

**Publisher:**Springer Science & Business Media

**ISBN:**1475743858

**Category:**Mathematics

**Page:**288

**View:**8190

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1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.

## A Course in Mathematical Logic for Mathematicians

**Author**: Yu. I. Manin

**Publisher:**Springer Science & Business Media

**ISBN:**1441906150

**Category:**Mathematics

**Page:**384

**View:**5711

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1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

## A Course in Mathematical Logic

**Author**: John Lane Bell,Moshe Machover

**Publisher:**Elsevier

**ISBN:**0080934749

**Category:**Logic, Symbolic and mathematical

**Page:**599

**View:**8537

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A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

## A Course in Model Theory

*An Introduction to Contemporary Mathematical Logic*

**Author**: Bruno Poizat

**Publisher:**Springer Science & Business Media

**ISBN:**1441986227

**Category:**Mathematics

**Page:**443

**View:**9998

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Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.

## A Course in Mathematical Logic

**Author**: John Lane Bell,Moshé Machover

**Publisher:**North-Holland

**ISBN:**N.A

**Category:**Computers

**Page:**599

**View:**3996

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A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

## A First Course in Mathematical Logic and Set Theory

**Author**: Michael L. O'Leary

**Publisher:**John Wiley & Sons

**ISBN:**0470905883

**Category:**Mathematics

**Page:**464

**View:**2381

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Rather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems. The study of logic andapplications is used throughout to prepare readers for further workin proof writing. Readers are first introduced tomathematical proof-writing, and then the book provides anoverview of symbolic logic that includes two-column logicproofs. Readers are then transitioned to set theory andinduction, and applications of number theory, relations, functions,groups, and topology are provided to further aid incomprehension. Topical coverage includes propositional logic,predicate logic, set theory, mathematical induction, number theory,relations, functions, group theory, and topology.

## First Course in Mathematical Logic

**Author**: Patrick Suppes,Shirley Hill

**Publisher:**Courier Corporation

**ISBN:**0486150941

**Category:**Mathematics

**Page:**288

**View:**3287

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Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.

## A Course on Mathematical Logic

**Author**: Shashi Mohan Srivastava

**Publisher:**Springer Science & Business Media

**ISBN:**1461457467

**Category:**Mathematics

**Page:**198

**View:**8446

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This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

## A Problem Course in Mathematical Logic

**Author**: Stefan Bilaniuk

**Publisher:**Orange Groove Books

**ISBN:**9781616100063

**Category:**Mathematics

**Page:**166

**View:**3555

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## Vorlesungen Über die Zahlentheorie der Quaternionen

**Author**: Adolf Hurwitz

**Publisher:**Springer-Verlag

**ISBN:**3642475361

**Category:**Mathematics

**Page:**76

**View:**2275

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

## Introduction to Mathematical Logic, Fourth Edition

**Author**: Elliott Mendelson

**Publisher:**CRC Press

**ISBN:**9780412808302

**Category:**Mathematics

**Page:**440

**View:**1531

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The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

## Principia Mathematica.

**Author**: Alfred North Whitehead,Bertrand Russell

**Publisher:**N.A

**ISBN:**N.A

**Category:**Logic, Symbolic and mathematical

**Page:**167

**View:**8320

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## A Mathematical Introduction to Logic

**Author**: Herbert Enderton,Herbert B. Enderton

**Publisher:**Elsevier

**ISBN:**0080496466

**Category:**Mathematics

**Page:**317

**View:**6231

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A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students

## Introduction to Mathematical Logic

*Extended Edition*

**Author**: MichaÅ Walicki

**Publisher:**World Scientific Publishing Company

**ISBN:**9814719986

**Category:**Mathematics

**Page:**304

**View:**4958

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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.

## A Course in Model Theory

**Author**: Katrin Tent,Martin Ziegler

**Publisher:**Cambridge University Press

**ISBN:**052176324X

**Category:**Mathematics

**Page:**248

**View:**4238

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This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

## Proofs and Fundamentals

*A First Course in Abstract Mathematics*

**Author**: Ethan D. Bloch

**Publisher:**Springer Science & Business Media

**ISBN:**1461221307

**Category:**Mathematics

**Page:**424

**View:**7855

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The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

## Mathematical Logic

**Author**: Joseph R. Shoenfield

**Publisher:**CRC Press

**ISBN:**135143330X

**Category:**Mathematics

**Page:**356

**View:**1114

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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: Part 1

*Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems*

**Author**: René Cori,Daniel Lascar

**Publisher:**OUP Oxford

**ISBN:**0191589772

**Category:**Mathematics

**Page:**360

**View:**2698

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Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.

## A Course in Mathematical Modeling

**Author**: Douglas D. Mooney,Randall J. Swift

**Publisher:**Cambridge University Press

**ISBN:**9780883857120

**Category:**Mathematics

**Page:**431

**View:**8508

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This book teaches elementary mathematical modeling.