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Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) [Englisch] [Taschenbuch]

Robert Goldblatt

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Kurzbeschreibung

28. April 2006 Dover Books on Mathematics
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes.
-- Dieser Text bezieht sich auf eine andere Ausgabe: Gebundene Ausgabe .

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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. -- Dieser Text bezieht sich auf eine andere Ausgabe: Gebundene Ausgabe .

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Amazon.com: 4.8 von 5 Sternen  5 Rezensionen
114 von 115 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Great introduction to the theory of toposes. 23. August 1998
Von Paul Corazza - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
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).
49 von 52 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Clear, concise, and well motivated. 24. Mai 2007
Von Trenton F. Schirmer - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
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.
23 von 25 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Enjoyable, though not as accessible as the author might hope. 17. November 2009
Von A.E.V. - Veröffentlicht auf Amazon.com
Format:Taschenbuch
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.
4 von 4 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Great introduction to category theory 21. April 2012
Von Joselector - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
I bought this book because I was interested in applying topos theory to quantum mechanics but I had no knowledge of category theory. Looking for books on Amazon this seemed to me perfect because it not only explains topos theory but also offers an introduction to category theory. This introduction can be followed without problems for those who had no prior knowledge of category theory, in addition the book's style is clear and concise, motivating each concept introduced. Of course you can not read it like a novel, the reader must work each example and exercise to gain mastery over the issues.
0 von 5 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Topoi 21. Oktober 2012
Von Parzhad - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
very well written book starts with nontechnical chapters to technical ones. I would recommend this book as an advanced reading for students and researchers in the field of philosophy of mathematics and foundations of mathematics and logic.
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