Mathematical Logic: Part 1

Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems

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Author: René Cori,Daniel Lascar

Publisher: OUP Oxford

ISBN: 0191589772

Category: Mathematics

Page: 360

View: 5971

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 Logic for Mathematicians

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Author: Yu. I. Manin

Publisher: Springer Science & Business Media

ISBN: 1441906150

Category: Mathematics

Page: 384

View: 956

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.

Introduction to Mathematical Logic

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Author: Hans Hermes

Publisher: Springer Science & Business Media

ISBN: 3642871321

Category: Mathematics

Page: 244

View: 2994

This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it. The book is meant primarily for mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculus. Today we know of many calculi which have this property.

Naive Mengenlehre

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Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 2223

Principia mathematica

Vorwort und Einleitungen

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: 9783518281932

Category: Mathematische Logik

Page: 167

View: 424

Discrete Mathematics for Computing

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Author: Peter Grossman

Publisher: Macmillan International Higher Education

ISBN: 1349139084

Category: Applied mathematics

Page: 289

View: 3346

Written in a clear and informal style aimed especially at students with a limited background in mathematics, this introduction to discrete mathematics presents the material that forms the essential mathematical background for studies in computing and information systems. The topics covered include number systems, logic, relations, functions, induction, recursion, Boolean algebra, combinatorics, graph theory and number theory. The text contains many examples of applications of the theory to problems in computing, including a chapter on the representation and manipulation of numbers in a computer, examples of the use of propositional logic in program design, a section discussing the relationship between the mathematical and programming concepts of a function, and a chapter on the estimation of the time complexity of algorithms. A feature of the book is the use of algorithms written in pseudo code in many examples throughout the text. The exercises at the end of each chapter provide both routine drill of basic techniques and more challenging problems designed to enhance and extend the students' understanding. Answers to most of the exercises are provided at the back of the book. With its emphasis on presenting mathematical concepts clearly and simply, without compromising on mathematical correctness, and with its frequent use of examples drawn from computing, Discrete Mathematics for Computing is suitable for use as a text for a one-semester introductory course in discrete mathematics, particularly for students who are undertaking studies in computing and information systems.

Gesetze der Form

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Author: George Spencer-Brown

Publisher: Joh. Bohmeier Verlag

ISBN: 9783890943213

Category: Algebraic logic

Page: 200

View: 1918

Logik für Dummies

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Author: Mark Zegarelli

Publisher: John Wiley & Sons

ISBN: 3527657444

Category: Mathematics

Page: 358

View: 4861

Logik ist die Basis von Wissenschaft, aber auch eine Br?cke von Wissenschaft zum Alltag. So einfach sie scheint, so anspruchsvoll ist sie im Detail. Mark Zegarelli f?hrt Sie in "Logik f?r Dummies" systematisch in die Logik ein. Vom Paradoxon ?ber symbolische Logik bis zur Syllogistik l?sst er nichts aus und zeigt Ihnen, wie man Argumente pr?ft. Er arbeitet dabei mit anschaulichen Beispielen und schafft es so, dieses abstrakte Thema den Lesern nicht nur verst?ndlich zu machen, sondern ihnen auch Wert und Nutzen von Logik aufzuzeigen. Eine Einf?hrung, die den Wissensdurst stillt und Lust auf mehr macht.

Strukturen der Syntax

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Author: Noam Chomsky

Publisher: Walter de Gruyter

ISBN: 3110813629

Category: Language Arts & Disciplines

Page: 136

View: 3984

Relationen und Graphen

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Author: Gunther Schmidt,Thomas Ströhlein

Publisher: Springer-Verlag

ISBN: 3642836089

Category: Mathematics

Page: 306

View: 8477

Dieses Buch gibt eine neuartige systematische Darstellung der Diskreten Mathematik; sie orientiert sich an Methoden der Relationenalgebra. Ähnlich wie man es sonst nur für die weit entwickelte Analysis im kontinuierlichen Fall und die Matrizenrechnung gewohnt ist, stellt dieses Buch auch für die Behandlung diskreter Probleme geeignete Techniken und Hilfsmittel sowie eine einheitliche Theorie bereit. Die einzelnen Kapitel beginnen jeweils mit anschaulichen und motivierenden Beispielen und behandeln anschließend den Stoff in mathematischer Strenge. Es folgen jeweils praktische Anwendungen. Diese entstammen der Semantik der Programmierung, der Programmverifikation, dem Datenbankbereich, der Spieltheorie oder der Theorie der Zuordnungen und Überdeckungen aus der Graphentheorie; sie reichen aber auch bis zu rein mathematischen "Anwendungen" wie der transfiniten Induktion. Im Anhang ist dem Buch eine Einführung in die Boolesche Algebra und in die Axiomatik der Relationenalgebra beigegeben, sowie ein Abriß der Fixpunkt- und Antimorphismen-Theorie.

Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

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Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 6831

Principia Mathematica.

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 5559

The Journal of Symbolic Logic

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Author: Alonzo Church

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 2135

Includes lists of members.