Logic is primarily about consistency - but not all types of consistency. For example if a man supports Arsenal one day and supports Spurs the next then he is fickle, but not necessarily illogical. The type of consistency which concerns logicians is not loyalty or justice or sincerity but compatibility of beliefs. Logic, therefore, involves studying the situations in which a sentence is true or valid and subsequently the rules which determine the validity or otherwise of a given argument.

Logic: An Introduction to Elementary Logic

Politics & Social Sciences

Hodges, Wilfrid

Philosophy

Penguin??Books

331p blue and white paperback with illustrated cover, hardly used, pages clean with chart and diagrams throughout, very good

Mathematical Logic (Oxford Texts in Logic)

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optinal sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science.

Chiswell, Ian

Oxford University Press

Model Theory (Encyclopedia of Mathematics and its Applications, Series Number 42)

Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a refe

Model Theory (Encyclopedia of Mathematics and its Applications) (Encyclopedia of Mathematics and its Applications, Series Number 42)

Reference

Encyclopedias & Subject Guides

Cambridge University Press

This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.

Building Models by Games (London Mathematical Society Student Texts, Series Number 2)

Science & Math

Mathematics

Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference.

This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

A Shorter Model Theory

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Books by Hodges, Wilfrid

See the best price to sell, buy, or rent books by Hodges, Wilfrid. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Logic: An Introduction to Elementary Logic

Logic: An Introduction to Elementary Logic

Mathematical Logic (Oxford Texts in Logic)

Model Theory (Encyclopedia of Mathematics and its Applications) (Encyclopedia of Mathematics and its Applications, Series Number 42)

Building Models by Games (London Mathematical Society Student Texts, Series Number 2)

Model Theory (Encyclopedia of Mathematics and its Applications, Series Number 42)

Building Models by Games (London Mathematical Society Student Texts, Series Number 2)

A Shorter Model Theory