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Provability, Computability and Reflection, Volume 98 (Studies in Logic and the Foundations of Mathematics), by Lev D. Beklemishev
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A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.
Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.
- Sales Rank: #12265368 in Books
- Published on: 1979-02-26
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 502 pages
Most helpful customer reviews
3 of 3 people found the following review helpful.
A classic exposition
By william harris
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.
8 of 9 people found the following review helpful.
Great introduction to category theory
By Joselector
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.
61 of 64 people found the following review helpful.
Clear, concise, and well motivated.
By Trenton F. Schirmer
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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