About this product

Product Identifiers

PublisherDover Publications, Incorporated

ISBN-100486477037

ISBN-139780486477039

eBay Product ID (ePID)80055187

Product Key Features

Number of Pages112 Pages

LanguageEnglish

Publication NameUndecidable Theories : Studies in Logic and the Foundation of Mathematics

Publication Year2010

SubjectHistory & Philosophy, Logic

TypeTextbook

AuthorRaphael M. Robinson, Alfred Tarski

Subject AreaMathematics

SeriesDover Books on Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Height0.4 in

Item Weight5.3 Oz

Item Length8.2 in

Item Width5.3 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2010-019851

Dewey Edition22

IllustratedYes

Dewey Decimal510.1

Table Of ContentI. A General Method in Proofs of Undecidability by Alfred Tarski I.1. Introduction I.2. Theories with standard formalization I.3. Undecidable and essentially undecidable theories I.4. Interpretability and weak interpretability I.5. Relativization of quantifiers I.6. Examples and applications II. Undecidability and Essential Undecidability in Arithmetic by Andrzej Mostowski, Raphael M. Robinson, and Alfred Tarski II.1. A summary of results; notation II.2. Definability in arbitrary theories II.3. Formalized arithmetic of natural numbers and its subtheories II.4. Recursiveness and definability in subtheories of arithmetic II.5. Undecidability of subtheories of arithmetic II.6. Extension of the results to other arithmetical theories and to various theories of rings III. Undecidability of the Elementary Theory of Groups by Alfred Tarski Bibliography Index

SynopsisThis book is well known for its proof that many mathematical systems -- including lattice theory and closure algebras -- are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.", This well-known book by the famed logician consists of three treatises: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups." 1953 edition., This graduate-level book is well known for its proof that many mathematical systems--including lattice theory, abstract projective geometry, and closure algebras--are undecidable. Based on research conducted from 1938 to 1952, it consists of three treatises by a prolific author who ranks among the greatest logicians of all time. The first article, "A General Method in Proofs of Undecidability," examines theories with standard formalization, undecidable theories, interpretability, and relativization of quantifiers. The second feature, "Undecidability and Essential Undecidability in Mathematics," explores definability in arbitrary theories and the formalized arithmetic of natural numbers. It also considers recursiveness, definability, and undecidability in subtheories of arithmetic as well as the extension of results to other arithmetical theories. The compilation concludes with "Undecidability of the Elementary Theory of Groups."

LC Classification NumberQA9.T33 2010

As told toMostowski, Andrzej