Hi. We stumbled across the following results, and wonder if anyone has already found them. They certainly feel like things that could have been done 50 to 100...
David Hobby's question about absolute nonassociativity prompts me to ask the following question that's been on my mind lately about some nonassociative...
Vaughan Pratt
pratt@...
Aug 18, 2007 7:01 am
435
i request you to tell me what is the exact definition of a Stone Space and some examples of it. with regards srinivas srinivasa rao...
Dear Srinivasa, Various equivalent definitions. Simplest probably is that it is a compact topological space such that for any two distinct points x and y,...
s.j.vickers@...
Aug 20, 2007 8:39 am
437
Dear all, I was recently given the following link, which I read with much enjoyment: http://www.math.rutgers.edu/~zeilberg/Opinion81.html Many congratulations...
Friedrich Wehrung
wehrung@...
Aug 26, 2007 11:53 am
438
Hello, as a new member of this group, I'd like to pose a question: Does anybody know, why the algebraic ring is called ring and the field called a field (in...
If my memory is accurate, the name "ringe" appeared first in 1915 or 1916 in a paper of Fraenkel. It is not in Weber's "Algebra", which does contain the word...
... Some of the information below is summarized from postings on the History of Math pages at The Math Forum @Drexel. (I haven't tried to verify its ...
Many thanks for the useful explanations! Meanwhile when sitting on the terrace I came across a tile, which is a physical body and an open set of atoms in my...
... The plausible speculation has my vote. Like the 2-element Boolean algebra, which generates its variety, the commutative ring of integers also generates...
Vaughan Pratt
pratt@...
Sep 18, 2007 7:41 pm
444
It is a theorem of category theory, but not of universal algebra, that every variety has an initial algebra. In category theory the initial algebra can be...
Vaughan Pratt
pratt@...
Sep 23, 2007 12:53 am
445
... The constants here of course referring to the constants (zeroary operations) of the clone, not just the constants of some basis, e.g. Z as the initial...
Vaughan Pratt
pratt@...
Sep 23, 2007 2:26 am
446
Hi, Vaughan, The universal algebra I learned came out of Slominski's little tract on infinitary operations. For him what was of interest were "equationally...
Fred E.J. Linton
flinton@...
Sep 23, 2007 3:32 am
447
Hi Vaughan, I am for the empty algebras. However I may note that even the deduction rules of classical logic are affected by that. For example "ForAll x (x=x)...
mhebert
mhebert@...
Sep 23, 2007 7:01 am
448
... The situation above is similar to the question whether the zero and the units are irreducibles (or primes) in Z by definition or not. The mankind has for...
Prohle Peter
prohlep@...
Sep 23, 2007 11:33 am
449
Dear Vaughan, [Executive summary: Yes.] The banning of empty carriers is historically a part not only of algebra, but also more generally of model theory in...
Steve Vickers
s.j.vickers@...
Sep 23, 2007 7:43 pm
450
Hi, my previous email is a bit more serious, read the new email below a bit more relaxed, take it easy. ... What was the question, your answer to what is...
Prohle Peter
prohlep@...
Sep 23, 2007 10:34 pm
451
I think Alice said it the best: Words mean what I choose them to mean. GG...
... Sometimes after an ill-chosen midnight email I re-read it in the morning and am reminded again of the wisdom of Celia's saying, "Mean words choose what I...
Vaughan Pratt
pratt@...
Sep 24, 2007 5:46 am
453
... Dear Vaughan, It's more subtle than that, because of the distinction between free and bound variables. It is only free variables that need to be...
Steve Vickers
s.j.vickers@...
Sep 24, 2007 9:15 am
454
... Dear Peter, Sorry, I was too terse. I meant to answer the question in the subject line, "Does every variety have an initial object?" Steve. (By the way,...
Steve Vickers
s.j.vickers@...
Sep 24, 2007 9:23 am
455
In the process of the design of the Common Algebraic Specification Language CASL (see www.cofi.info), we have had the very same discussion. CASL has a...
I have been deleting most of the E-mails on this subject because I think they miss the need to be clear. Most mathematicians need to think about what an author...
In order to be able to construe Act-S, the category of all right S- acts where S is a monoid, as a complete category it is necessary to allow the empty S-act....
As a semigrouper and from a purely practical standpoint, not allowing an empty semigroup would mean that there are semigroups whose set of subsemigroups does...
Katherine Thom
thomk@...
Sep 24, 2007 5:49 pm
460
... This is a key observation (including the subject of the email)! I find the whole discussion too technical ===> we lost ourselves in the thechnical details....
Prohle Peter
prohlep@...
Sep 24, 2007 7:51 pm
461
... Steve Vickers ... that n ... Steve, I am shocked, shocked. :) Translating this algebra-speak into language-for-the-rest-of-us: ok, so every natural number...
Vaughan Pratt
pratt@...
Sep 24, 2007 8:28 pm
462
Melvin Henriksen <henriksen@...> wrote: Deductions involving the empty set usually require thought, and adding a few...
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