- Paperback: 304 pages
- Publisher: Cambridge University Press; Reprint edition (Mar 25 1988)
- Language: English
- ISBN-10: 0521356539
- ISBN-13: 978-0521356534
- Product Dimensions: 2.3 x 1.5 x 0.2 cm
- Shipping Weight: 454 g
- Amazon Bestsellers Rank: #564,943 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Details |
Product Description
Review
"...important monograph...very clearly written..." SciTech Book News
"...a readable and timely account of important results, most of which were not previously available in book form." London Mathematical Society
"[The authors] present their material as persuasively and as lucidly as possible. In addition, they have included many useful exercises and illuminating historical and philosophical remarks, which should make the book attractive to an audience not confined to the already expert. This is an excellent and timely work on a subject that is assuming an increasingly important role in the foundations of mathematics." J.L. Bell, Journal of Symbolic Logic
"...a readable and timely account of important results, most of which were not previously available in book form." London Mathematical Society
"[The authors] present their material as persuasively and as lucidly as possible. In addition, they have included many useful exercises and illuminating historical and philosophical remarks, which should make the book attractive to an audience not confined to the already expert. This is an excellent and timely work on a subject that is assuming an increasingly important role in the foundations of mathematics." J.L. Bell, Journal of Symbolic Logic
Product Description
In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludeds with a set of exercises.
Inside This Book
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First Sentence
In Part 0 we recall the basic background in category theory which may be required in later portions of this book. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
In Part 0 we recall the basic background in category theory which may be required in later portions of this book. Read the first page
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Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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5.0 out of 5 stars (1 customer review)
25 of 32 people found the following review helpful
5.0 out of 5 stars
This is definitely Higher!, Dec 14 2000
By A Customer - Published on Amazon.com
This review is from: Introduction to Higher-Order Categorical Logic (Paperback)
I was looking for a book for my girlfriend this Christmas and stumbled upon this one. At first I thought it would be too light but was I ever mistaken!! This book is so high that it would make Jack Kerouac dizzy. It begins with a treatment of basic category theory and ccc's and then goes on to present toposes and intuitionistic type theory. The authors take care to annotate their turnstile with the set of free variables (Hah! I bet you thought I had no idea what this book was about!) so that they can deal with empty types in a reasonable way. The treatment of presheaf models is very lucid and the discussion of internal languages and lambda-calculi is excellent. In fact many papers of Koymans are just exercises from this book worked out. The book is slightly out of date, no treatment of linear logic or symmetric monoidal-closed categories. Overall this book is highly recommended for the beginner and expert alike.
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