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    Undecidable Theories: Studies in Logic and the Foundation of Mathematics (Dover Books on Mathematics) (Paperback) By (author) Alfred Tarski, With Andrzej Mostowski, With Raphael R. Robinson

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    DescriptionThis 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."


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    Title
    Undecidable Theories
    Subtitle
    Studies in Logic and the Foundation of Mathematics
    Authors and contributors
    By (author) Alfred Tarski, With Andrzej Mostowski, With Raphael R. Robinson
    Physical properties
    Format: Paperback
    Number of pages: 112
    Width: 135 mm
    Height: 208 mm
    Thickness: 10 mm
    Weight: 159 g
    Language
    English
    ISBN
    ISBN 13: 9780486477039
    ISBN 10: 0486477037
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    Nielsen BookScan Product Class 3: S7.9T
    B&T Modifier: Region of Publication: 01
    BIC subject category V2: PBCD
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    Libri: I-MA
    Warengruppen-Systematik des deutschen Buchhandels: 26220
    BISAC V2.8: MAT014000
    DC21: 510.1
    BISAC V2.8: MAT018000
    BIC subject category V2: PBG
    DC22: 510.1
    LC subject heading: ,
    LC classification: QA9 .T33 2010
    Dover Categories: , ,
    Thema V1.0: PBG, PBCD
    Edition statement
    Dover.
    Publisher
    Dover Publications Inc.
    Imprint name
    Dover Publications Inc.
    Publication date
    24 September 2010
    Publication City/Country
    New York
    Table of contents
    I.  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