A Concise Introduction to Mathematical Logic

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Sprache: Englisch

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Beschreibung

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, Gödel, 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 Gödel¿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 Gödel¿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.

Zusammenfassung

Chapter summaries

Section summaries

Detailed illustrations

Study guides at the ends of sections

Exercises at the ends of chapters or sections

Solutions to selected exercises in the book

A separate solutions manual (on the Internet)

Instructor's manual with solutions and teaching guides

Includes supplementary material: [...]

Inhaltsverzeichnis

Propositional Logic.- First-Order Logic.- Complete logical Calculi.- Foundations of Logic Programming.- Elements of Model Theory.- Incompleteness and Undecidability.- On the Theory of Self-Reference.

Details

Erscheinungsjahr:	2009
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxii 320 S. 25 s/w Illustr. 320 p. 25 illus.
ISBN-13:	9781441912206
ISBN-10:	1441912207
Sprache:	Englisch
Herstellernummer:	12616268
Einband:	Kartoniert / Broschiert
Autor:	Rautenberg, Wolfgang
Auflage:	3rd edition 2010
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 168 x 19 mm
Von/Mit:	Wolfgang Rautenberg
Erscheinungsdatum:	17.12.2009
Gewicht:	0,581 kg