Logic and Structure (Universitext) 5th Edition by Dirk van Dalen (PDF)

Description

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 Gödel’s famous incompleteness theorem. 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-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. 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 Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel’s first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐My Logic lecturer specified the 4th edition of this book, but I got this one. On closer inspection there’s an extra chapter at the start, so old listing 1.4 is 2.4 in this edition. Other than that there are a few corrections and on extra subsection. Students have no fear about buying this one instead of 4th ed.

⭐This book is one of the standard textbooks for an introductory course on logic. The book excels at the following topics: classical predicative logic, the completeness and compactness results for first order logic, intuitionist logic, and the Godel theorems. Besides that, the author includes a short section o second order logic, and cuts (but for those two topics you can find better books out there).Mathematical logic studies the language used for mathematics at a foundational level. Such language is not “necessary” for the understanding of most mathematics (meaning that professional mathematicians can express their ideas in “english plus mathematical jargon”. However, if you are interested in understanding the foundational aspects of mathematics, learning logic would be the first step. If that’s your goal, this book would give you all you need to get started.Lastly, this book requires some degree of mathematical maturity usually reached around your first couple of classes involving formal mathematical proofs. I believe that’s the intended audience for the book. So, if you are interested in logic for philosophical reasons, or just for entertainment, perhaps you’d benefit more from reading a book intended for philosophy or for dilettantes.

⭐spiega dalle basi

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