A Course In Mathematical Logic

Author : Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 48,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475743852

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A Course in Mathematical Logic by Yu.I. Manin Pdf

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.

Author : Stefan Bilaniuk
Publisher : Orange Groove Books
Page : 166 pages
File Size : 47,5 Mb
Release : 2009-09-01
Category : Mathematics
ISBN : 1616100060

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A Problem Course in Mathematical Logic by Stefan Bilaniuk Pdf

Author : Shashi Mohan Srivastava
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 40,9 Mb
Release : 2013-01-16
Category : Mathematics
ISBN : 9781461457466

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A Course on Mathematical Logic by Shashi Mohan Srivastava Pdf

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.

Author : Bruno Poizat
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781441986221

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A Course in Model Theory by Bruno Poizat Pdf

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.

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 49,9 Mb
Release : 2015-09-14
Category : Mathematics
ISBN : 9781118548011

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A First Course in Mathematical Logic and Set Theory by Michael L. O'Leary Pdf

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

Author : Patrick Suppes,Shirley Hill
Publisher : Courier Corporation
Page : 308 pages
File Size : 50,7 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486150949

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First Course in Mathematical Logic by Patrick Suppes,Shirley Hill Pdf

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.

Author : Zofia Adamowicz,Pawel Zbierski
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 53,9 Mb
Release : 2011-09-26
Category : Mathematics
ISBN : 9781118030790

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Logic of Mathematics by Zofia Adamowicz,Pawel Zbierski Pdf

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.

Author : Richard E. Hodel
Publisher : Courier Corporation
Page : 514 pages
File Size : 49,5 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497853

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An Introduction to Mathematical Logic by Richard E. Hodel Pdf

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461572886

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Introduction to Mathematical Logic by Elliot Mendelsohn Pdf

This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 42,9 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

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A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Author : Mark Kac,Stanislaw M. Ulam
Publisher : Courier Corporation
Page : 189 pages
File Size : 54,9 Mb
Release : 1992-01-01
Category : Philosophy
ISBN : 9780486670850

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Mathematics and Logic by Mark Kac,Stanislaw M. Ulam Pdf

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Author : Joseph R. Shoenfield
Publisher : CRC Press
Page : 281 pages
File Size : 47,8 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781351433303

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Mathematical Logic by Joseph R. Shoenfield Pdf

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.

Author : Stephen Cole Kleene
Publisher : Courier Corporation
Page : 416 pages
File Size : 43,8 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486317076

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Mathematical Logic by Stephen Cole Kleene Pdf

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.

Author : J.L. Bell,Moshé Machover
Publisher : North Holland
Page : 632 pages
File Size : 48,5 Mb
Release : 1977-01-15
Category : Computers
ISBN : UOM:39015040409156

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A Course in Mathematical Logic by J.L. Bell,Moshé Machover Pdf

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.

Author : Herbert B. Enderton
Publisher : Elsevier
Page : 330 pages
File Size : 47,7 Mb
Release : 2001-01-23
Category : Computers
ISBN : 9780080496467

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A Mathematical Introduction to Logic by Herbert B. Enderton Pdf

A Mathematical Introduction to Logic