A Concise Introduction to Mathematical Logic (Universitext)

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9781441912206: A Concise Introduction to Mathematical Logic (Universitext)

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.

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From the Back Cover:

Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for mathematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy.

This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization techniques to set theory. Chapter 3 is partly of descriptive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics.

The remaining chapters contain basic material on logic programming for logicians and computer scientists, model theory, recursion theory, Gödel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. Each section of the seven chapters ends with exercises some of which of importance for the text itself. There are hints to most of the exercises in a separate file Solution Hints to the Exercises which is not part of the book but is available from the author’s website.

Review:

From the reviews of the third edition:

“Wolfgang Rautenberg’s A Concise Introduction to Mathematical Logic is a pretty ambitious undertaking, seeing that at the indicated introductory level it covers ‘classical material ... and Godel’s incompleteness theorems, as well as some topics motivated by applications, such as chapter on logic programming’ (from the Foreword by Lev Beklemishev). ... The third edition ... is a fine piece of scholarship and will more than repay the efforts of the committed student who chooses this means as an entry into modern mathematical logic.” (Michael Berg, The Mathematical Association of America, June, 2010)

“This is essentially the English translation of the third edition of the German version [Einführung in die mathematische Logik. Ein Lehrbuch. Wiesbaden: Vieweg+Teubner (2008; Zb1 1152.03-002)] of this well-written textbook ... . The book remains one of the most recommendable introductions into mathematical logic for mathematicians, and well-suited for computer scientists too.” (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1185, 2010)

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Wolfgang Rautenberg
Editorial: Springer-Verlag New York Inc., United States (2009)
ISBN 10: 1441912207 ISBN 13: 9781441912206
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Descripción Springer-Verlag New York Inc., United States, 2009. Paperback. Estado de conservación: New. 3rd ed. 2010. Language: English . Brand New Book ***** Print on Demand *****.by Lev Beklemishev, Moscow The ?eld of mathematical logic-evolving around the notions of logical validity, provability, and computation-was created in the ?rst half of the previous century by a cohort of brilliant mathematicians and philosophers such as Frege, Hilbert, Godel, Turing, Tarski, Malcev, Gentzen, and some others. The development of this discipline is arguably among the highest achievements of science in the twentieth century: it expanded mat- matics into a novel area of applications, subjected logical reasoning and computability to rigorous analysis, and eventually led to the creation of computers. The textbook by Professor Wolfgang Rautenberg is a well-written - troduction to this beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Godel s incompleteness theorems, as well as some topics motivated by appli- tions, such as a chapter on logic programming. The author has taken great care to make the exposition readable and concise; each section is accompanied by a good selection of exercises. A special word of praise is due for the author s presentation of Godel s second incompleteness theorem, in which the author has succeeded in giving an accurate and simple proof of the derivability conditions and the provable ? -completeness, a technically di?cult point that is usually 1 omittedintextbooksofcomparablelevel. Thisworkcanberecommended to all students who want to learn the foundations of mathematical logic. Nº de ref. de la librería AAV9781441912206

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Descripción Springer Verlag, 2009. Paperback. Estado de conservación: Brand New. 3rd edition. 319 pages. 9.25x6.50x0.75 inches. In Stock. Nº de ref. de la librería __1441912207

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Descripción Springer-Verlag New York Inc., United States, 2009. Paperback. Estado de conservación: New. 3rd ed. 2010. Language: English . Brand New Book ***** Print on Demand *****. by Lev Beklemishev, Moscow The ?eld of mathematical logic-evolving around the notions of logical validity, provability, and computation-was created in the ?rst half of the previous century by a cohort of brilliant mathematicians and philosophers such as Frege, Hilbert, Godel, Turing, Tarski, Malcev, Gentzen, and some others. The development of this discipline is arguably among the highest achievements of science in the twentieth century: it expanded mat- matics into a novel area of applications, subjected logical reasoning and computability to rigorous analysis, and eventually led to the creation of computers. The textbook by Professor Wolfgang Rautenberg is a well-written - troduction to this beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Godel s incompleteness theorems, as well as some topics motivated by appli- tions, such as a chapter on logic programming. The author has taken great care to make the exposition readable and concise; each section is accompanied by a good selection of exercises. A special word of praise is due for the author s presentation of Godel s second incompleteness theorem, in which the author has succeeded in giving an accurate and simple proof of the derivability conditions and the provable ? -completeness, a technically di?cult point that is usually 1 omittedintextbooksofcomparablelevel. Thisworkcanberecommended to all students who want to learn the foundations of mathematical logic. Nº de ref. de la librería AAV9781441912206

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Descripción Springer, 2009. Paperback. Estado de conservación: NEW. 9781441912206 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Nº de ref. de la librería HTANDREE0294502

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