Books : Toposes and Local Set Theories: An Introduction (Dover Books on Mathematics)

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Author name: J. L. Bell

: Toposes and Local Set Theories: An Introduction (Dover Books on Mathematics)
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Type of bind: Paperback
Dewey Decimal Number: 512.62
EAN num: 9780486462868
ISBN number: 0486462862
Label: Dover Publications
Manufacturer: Dover Publications
Quantity: 1
Page Count: 288
Printing Date: January 11, 2008
Publishing house: Dover Publications
Sale Popularity Level: 233670
Studio: Dover Publications



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Editor's Notes and Comments:

Product Description:
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.




Customer Reviews
User popularity level: out of 5 stars

Rated by buyers 3 out of 5 stars - 57 is Grothendeick's prime
The Bourbaki structuralist approach is said by Amir C, Aczel to be:
"overly formal . too abstract. and much more rigorous than necessary. thus making it unnecessarily difficult to read and understand mathematics."
My immediate reaction / objection to this book is that this level of abstraction removes categories from the 'real world' reference of a new mathematics for ordinary people. For this approach to be effective one must already have had set theory, algebraic theory, symbolic logic and specifically for this book, the theory of topological neighborhoods.
Those qualifications put this approach to category theory above what is taught to graduates in the physical sciences in general and removes it to graduates( or very advanced undergraduates) in mathematics alone.
I don't think this could be what Grothendieck had in mind
when he wanted to put category theory in the place of set theory
as the base of mathematics in teaching.
I'll give an example of the kind this author fails vividly to give!
Category:
mathematics authors
sub categories:
1) humanist
2) antihumanist ( structuralist)
arrows:
1) theoretical examples
2) concrete examples
Now to make a Lewis Carroll ( Charles Dodgson) type sentence using
this:
A mathematics author is an antihumanist if the only examples he gives in his text are theoretical examples.
A mathematics author is an humanist if he gives both theoretical and concrete examples.
I'll let you figure out in which category I think J. L. Bell belongs.





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