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Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) Revised ed. Edition

4.7 out of 5 stars 7 customer reviews
ISBN-13: 080-0759450268
ISBN-10: 0486450260
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  • Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
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Editorial Reviews

About the Author

Robert Goldblatt is a Professor of Pure Mathematics at the Victoria University of Wellington, New Zealand, and a Fellow of the Royal Society of New Zealand. He has served as the Co-ordinating Editor of the Journal of Symbol Logic and has been a Managing Editor of Studia Logica for the past two decades.
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 592 pages
  • Publisher: Dover Publications; Revised ed. edition (April 28, 2006)
  • Language: English
  • ISBN-10: 0486450260
  • ISBN-13: 978-0486450261
  • Product Dimensions: 5.5 x 1.1 x 8.5 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #635,828 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Hardcover
When Goldblatt's book first hit the stands, it was blasted by reviewers who had a geometric predilection. They claimed that Goldblatt had trivialized this essentially rich geometric subject by giving a set-theoretic treatment.
I became fascinated with topos theory in the summer of 1989. My only experience with category theory at that time was some dabbling that every graduate student gets in studying modules and in functional analysis. I didn't have much background in algebraic topology where the subject is usually developed considerably further.
Frankly, I found Goldblatt's "gentle" approach to categorical concepts and the concept of a topos very rewarding. I worked through most of the book in a summer, and was fully prepared to take on the more advanced texts at that point. Later, I had the opportunity to teach topos theory at the graduate level to people with backgrounds similar to mine (i.e., without a strong background in category theory). We worked through most of Goldblatt's book in the first semester and I guarantee that all the students were very grateful, as I had been, for Goldblatt's approach to the subject.
The book is well written, accessible to graduate students, filled with fun and often challenging exercises, and packed with references. In my opinion, it is the right place to start if you want to become proficient in topos theory (and you don't already have significant proficiency in category theory).
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Format: Paperback Verified Purchase
I have only read the first seventy pages of this book, but so far it is excellent. The character of the book can be likened to Kleene's "Introduction to Metamathematics" or "Mathematical Logic." The subject is well motivated by brief philosophical discussions, but the philosophy is not allowed to interrupt the flow of mathematical development. There are few exercises, but enough for the casual reader to check from time to time that he or she is understanding the material. The exposition itself is perfectly clear and concise, by my lights. Nothing important is skipped--one does not need to fill in the blanks in proofs--yet the book moves at a good pace. The focus of the book is on the development of Category theory in relation to its applications in logic. For this reason it is probably of more interest to a logician or a philosopher than to a computer scientist. Indeed, for the logician who is interested in Category theory this book cannot be missed. To put it bluntly, Goldblatt strikes me as a superior mind, even his brief remarks on set theory were enlightening. The book has been (to this point, at least) a very enjoyable read.
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Format: Paperback
I came to this book with an interest in philosophy of mathematics, formal semantics, and non-classical logics, attracted to the author's stated goals to make category theory and its implications available to both the mathematically and philosophically inclined by requiring very little background in set theory or mathematics. I have a fairly good grasp of first order logic, and know enough set theory to talk about things like Kripke semantics in a general fashion, and I find this book challenging. The author defines things like a limit on a diagram (fairly early in the book) and doesn't make it clear to me what the significance of the concept is supposed to be.

I do still find it full of suggestive and interesting ideas, and the author is clearly knowledgeable and enthusiastic. A general picture does emerge in the less formal discussions at the beginnings of the chapters, so flipping around a little can help you get an idea for the context. But ultimately I think this is still more accessible to graduate level math students, and I'm giving it a four star review because so far as I can tell, it succeeds in its technical aspects, and mainly fails only in reaching its entire stated audience.
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Format: Paperback Verified Purchase
This is an interesting addition to the field that was well ahead of the pack. Not as well written as Lawvere's later "Conceptual Mathematics" it covers more territory and becomes quite dense in its development of category theory which is now well established applied mathematics whose pure roots in sets is still evident.
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