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Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics) Paperback – March 25, 1988

ISBN-13: 978-0521356534 ISBN-10: 0521356539

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Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics) + Category Theory (Oxford Logic Guides)
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Product Details

  • Series: Cambridge Studies in Advanced Mathematics (Book 7)
  • Paperback: 304 pages
  • Publisher: Cambridge University Press (March 25, 1988)
  • Language: English
  • ISBN-10: 0521356539
  • ISBN-13: 978-0521356534
  • Product Dimensions: 6 x 0.7 x 9 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,018,929 in Books (See Top 100 in Books)

Editorial Reviews

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

Book Description

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

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Most Helpful Customer Reviews

31 of 41 people found the following review helpful By A Customer on December 14, 2000
Format: 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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