A Course in Mathematical Logic for Mathema...

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Beschreibung

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.

Zusammenfassung

Contains a new chapter on categorical approach to theory of computations, quantum computations, and P/NP problem

New chapter containing basic results of Model Theory and its applications to mainstream mathematics

Presents several highlights of mathematical logic of the 20th century including Gödel's and Tarski's Theorems, Cohen's Theorem on the independence of Continuum Hypothesis

Complete proof of Davis-Putnam-Robinson-Matiyasevich theorem

Discusses Kolmogorov complexity

Includes supplementary material: [...]

Inhaltsverzeichnis

PROVABILITY.- to Formal Languages.- Truth and Deducibility.- The Continuum Problem and Forcing.- The Continuum Problem and Constructible Sets.- COMPUTABILITY.- Recursive Functions and Church#x2019;s Thesis.- Diophantine Sets and Algorithmic Undecidability.- PROVABILITY AND COMPUTABILITY.- G#x00F6;del#x2019;s Incompleteness Theorem.- Recursive Groups.- Constructive Universe and Computation.- MODEL THEORY.- Model Theory.

Details

Erscheinungsjahr:	2012
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 384 S. 12 s/w Illustr. 384 p. 12 illus.
ISBN-13:	9781461424796
ISBN-10:	1461424798
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Manin, Yu. I.
Übersetzung:	Koblitz, Neal
Auflage:	2nd edition 2010
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 22 mm
Von/Mit:	Yu. I. Manin
Erscheinungsdatum:	03.03.2012
Gewicht:	0,61 kg