Description
Springer Logic and Structure by Dirk Van Dalen
Dirk van Dalen's popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Goedel's famous incompleteness theorem. _x000D__x000D_Propositional and predicate logic are presented in an easy-to-read style using Gentzen's natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Loewenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. _x000D__x000D_In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Goedel translation, the disjunction and existence property are also included. _x000D__x000D_The last chapter on Goedel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. _x000D__x000D_This new edition has been properly revised and contains a new section on ultra-products._x000D_ Table of contents :- _x000D_
Introduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normalization.- Goedel's theorem._x000D_