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Introduction to Metalogic by Aladdin M. Yaqub (2014, Trade Paperback)

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Introduction to Metalogic, Paperback by Yaqub, Aladdin M., ISBN 1554811716, ISBN-13 9781554811717, Brand New, Free shipping in the US The meta-theory of classical logic is presented with unparalleled clarity in this rigorous new book.

About this product

Product Identifiers

PublisherBroadview Press

ISBN-101554811716

ISBN-139781554811717

eBay Product ID (ePID)3057265949

Product Key Features

Number of Pages344 Pages

Publication NameIntroduction to Metalogic

LanguageEnglish

SubjectLogic

Publication Year2014

TypeTextbook

Subject AreaMathematics, Philosophy

AuthorAladdin M. Yaqub

FormatTrade Paperback

Dimensions

Item Height0.6 in

Item Length9 in

Item Width7 in

Additional Product Features

Intended AudienceScholarly & Professional

Dewey Edition23

ReviewsComments: "This is an excellent text in intermediate logic that should be warmly received by students. The well-paced exposition is remarkably clear. The choice of material, including remarks on the philosophical significance of the principal theorems and welcome sections on Second-Order logic, seems just right. And the ample exercises at the end of each chapter, which range from easy to difficult, not only test the reader's understanding, but move the subject forward. Highly recommended." - David Keyt, Research Professor, University of Arizona; Professor Emeritus, University of Washington "An Introduction to Metalogicprovides extensive coverage of the usual meta-theoretic results concerning the standard logical systems. It covers the completeness theorems, compactness, the Löwenheim-Skolem theorems, and the incompleteness of arithmetic. There is also a good sketch of more advanced topics, giving the enthusiastic reader and student incentive to keep studying the field. As with Professor Yaqub's earlier logic text, An Introduction to Logical Theory, the presentation is clear and straightforward." - Stewart Shapiro, Ohio State University "Yaqub has produced a pedagogically sensitive, yet completely rigorous tour of the introductory metalogical terrain. His textbook will be welcomed by instructors in philosophy, mathematics, computer science and linguistics who endeavor to offer their students something more substantial than standard introductory logic." - Kai Wehmeier, University of California, Irvine

TitleLeadingAn

IllustratedYes

Dewey Decimal160

Table Of ContentIntroduction Chapter One: First-Order Predicate Logic (PL) 1.1 The Syntax of PL The basic vocabulary of PL PL terms PL formulas Bound and free variables and PL sentences 1.2 The Semantics of PL PL interpretations Examples of PL interpretations Objectual and substitutional quantification The size of a PL interpretation The truth conditions of PL sentences Possible objections to substitutional quantification and replies 1.3 Logical Concepts in PL Definition of a PL argument Validity and logical consequence Definition of a valid argument Definition of an invalid argument Definition of a valid sentence Definition of a contradictory sentence Definition of a contingent sentence Definition of logically equivalent sentences Definition of a satisfiable set Definition of an unsatisfiable set Decidable and semidecidable concepts 1.4 PL Proof Theory The notion of formal derivation The statements of the Soundness and Completeness Theorems for PL Corollaries of the Soundness and Completeness Theorems The structure and application of inference rules The Natural Deduction System (NDS) A justification for the rule Explosion The Gentzen Deduction System (GDS) 1.5 Exercises Solutions to the Starred Exercises Chapter Two: Resources of the Metatheory 2.1 Linguistic and Logical Resources The metatheory of PL The language of the metatheory Logical resources 2.2 Arithmetical Resources The structure of the natural numbers The Principle of Mathematical Induction 2.3 Set-Theoretic Resources Basic concepts and principles Russell''s Paradox Relations and functions Cardinalities of sets Cantor''s Diagonal Argument 2.4 An Economical Version of PL Expressive completeness The Mini Deduction System (MDS) 2.5 Exercises Solutions to the Starred Exercises Chapter Three: The Soundness and Completeness Theorems 3.1 The Soundness Theorem 3.2 The Completeness Theorem An equivalent formulation of the Completeness Theorem Lindenbaum''s Lemma Henkin sets Henkin interpretations of Henkin sets without the identity predicate Henkin interpretations of Henkin sets with the identity predicate 3.3 The Compactness Theorem The Compactness Theorem The Finite-Satisfiability Theorem 3.4 Elementary Equivalence and Isomorphism 3.5 Properties of PL Sets PL theories Axiomatizable PL theories Complete and categorical PL sets 3.6 The Löwenheim-Skolem Theorem A proof of the theorem Skolem''s Paradox 3.7 Exercises Solutions to the Starred Exercises Chapter Four: Computability 4.1 Effective Procedures and Computable Functions 4.2 Turing Computability Turing machines An example Instruction lines and diagrams of Turing machines The zero, successor, and addition functions Turing-computable functions and Church''s Thesis Decidable and semidecidable sets 4.3 The Halting Problem 4.4 Partial Recursive Functions 4.5 Exercises Solutions to the Starred Exercises Chapter Five: The Incompleteness Theorems 5.1 Peano Arithmetic 5.2 Representability in Peano Arithmetic 5.3 Arithmetization of the Metatheory 5.4 Diagonalization and the First Incompleteness Theorem The Diagonalization Lemma Gödel''s First Incompleteness Theorem 5.5 Consequences of Diagonalization and Incompleteness The undecidability of consistent extensions of Peano Arithmetic Tarski''s Indefinability Theorem Church''s Undecidability Theorem 5.6 The Incompleteness of Second-Order Predicate Logic Second-Order Predicate Logic (PL²) Second-Order Peano Arithmetic PL2 and the Compactness Theorem The incompleteness of PL² 5.7 Gödel''s Second Incompleteness Theorem Hilbert''s Program The Provability Conditions 5.8 Exercises Solutions to the Starred Exercises Index

SynopsisAn Introduction to Metalogicis a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between., The meta-theory of classical logic is presented with unparalleled clarity in this rigorous new book.