Book Description
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis. ... Read more

Book Description
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science.This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic. ... Read more

Customer Reviews (1)

OK but Hard
You'll find this very hard unless you are a competent math major at one of the better universities. Similar to Elliot Mendelson's text, but not quite as good. Good chapter on Boolean algebra as a
piece of pure math; Halmos and Givant is gentler, though.

Interesting topic covered: the resolution so dear to the AI crowd. Unlike most mathematicians, Cori and Lascar have time for
the way computer scientists think. At the same time, this book does not cover tableau methods (see Smullyan), natural deduction, Genzen's ideas, and so on. For pure logic at the advanced undergrad level, you're better off with Bostock.

Haven't seen Part II, so cannot comment on the treatment of set theory. This is something Mendelson and Machover already do well. ... Read more

Book Description
Recursive Functions and Metamathematics deals withproblems of the completeness and decidability of theories, using asits main tool the theory of recursive functions. This theory is firstintroduced and discussed. Then Gödel's incompleteness theoremsare presented, together with generalizations, strengthenings, and thedecidability theory. The book also considers the historical andphilosophical context of these issues and their philosophical andmethodological consequences. Recent results and trends have beenincluded, such as undecidable sentences of mathematical content,reverse mathematics. All the main results are presented in detail. Thebook is self-contained and presupposes only some knowledge ofelementary mathematical logic. There is an extensive bibliography.
Readership: Scholars and advanced students of logic,mathematics, philosophy of science. ... Read more

Book Description
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science.This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic. ... Read more

Book Description
Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra.In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them. An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems. ... Read more