Re: Elementary Topos...book

[Ionel <***>]

Tim:

1. Yes, that's the site that i know of. I did print it page by page.
It's most definitely worth the effort.


On Tue, 25 May 2004 09:43:57 -0400, Tim Gwinn <***> wrote:

>> -----Original Message-----
>> From: ROSEN Forum []On Behalf Of Ionel
>> Sent: Monday, May 24, 2004 10:51 PM
>> Subject: Re: Elementary Topos...book
>--snip--
>> Tim:
>>

>
>
1. >> Especially since one can download the very easy to follow
>> Goldblatt's Topos book (out of print now) from the web for free...Can it
>> get much better than that?! It's a fully-fledged book, still current, but
>> mostly emphasizing the logical aspects more than the categorical ones.
>
>
>Do you mean "Topoi : the categorical analysis of logic"? I found it as a
>page-by-page viewable document at Cornell:
>http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?
did=Gold010
>&seq=4
>
>Do you know of a site where it can be downloaded as a complete book? I'd
>like to add the link to my website.



2.  However, I'm really happy with Saunders MacLane's & I'M's "Geometry,
>> Sheaves and Topos.." that I mentioned to you before, and it's new
>> at around
>> $40; that's a very serious book, with very nice explanations of
>> how and why
>> so? It is a real bargain; I noted that on occasion doesn't quite agree,
or
>> contradicts completely views expressed by Robert in his "Essays..." about
>> matematics and logics.
>
>
>I almost got this one too....but I decided to budget the $$ a bit. :) I am
>very curious: in what ways do MacLane/Rosen disagree?
>

2. As you know, Tim, Saunders MacLane is the first category theorist/
mathematician who invented/ discovered categories together with Eilenberg,
sometimes between 1942 and 1945.  How do they disagree? Well, basically
when it comes to Logic applications to maths and especially categories.
Robert chose impredicativities, unlike Saunders, who--like most
mathematicians and logicians today, prefers Heyting Logic (Intuitionistic)
algebras to Boolean, and avoid the "tertium non datur"--Excluded Third
Principle of "classical" logic. Furthermore, one can think of a Topos as a
"generalized space" says Prof. Saunders MacLane far more general than
either the concept of set , or the category of sets. Robert wrote to me
around 1973 that "the category of sets is the most general from a
mathematical standpoint"... and this is why he chose it as a formalization
for (M,R)-Systems and Biological Systems. Even in 1973, that statement was
no longer accepted by the mathematicians working in Category theory.
Today, it would seem that a Topos is seen as the concept that lies at the
foundation of Mathematics, and maybe more... Therefore, I am looking at
Topos as a means of representing biological systems with a view to entail
function in Heyting Logic/algebras. For finite models also the Lukn--
the category of Lukasiewicz algebras-- is capable of entailing function in
Genetic Networks without impredicativities that appear when limiting
oneself to Boolean logic. Last-but-not-least, in our second paper in 1969,
we introduced sequences or limits of commutative diagrams of relations
between Logic, Models and Categories to formalize the modeling process.
I noticed that you have now the same idea that we introduced 35 years ago
in our second paper in BMB (1969, except for the fact that we gave this
idea a precise form, on the first page of that published article. I have no
doubt that Robert was aware of the article.


3. >> You must now that Saunders got his degree in 1929,
>> and still publishing such a fantastically good book in 1996/7!!! Maybe
the
>> book of the Century with Robert's "Life Itself"? What do you think?

I have  received now the "...Working Mathematician"  also by Saunders; at
$$20 it is v. good value since it is quite useful.
looks like another great book along with his older (abstract) Algebra.
>> Please see my other comments also today on Topos.

Regards and happy Topos/Topoi readings!

Ionel