There is a decent introduction in Peter Johnstone's "Stone Spaces" (Cambridge University Press), written from the point of view that completely distributive...
Steve Vickers
s.j.vickers@...
Nov 24, 2003 12:27 pm
188
I have a problem related to duality theory for Heyting algebras. It is known that open sets of a topological space form a Heyting algebra under natural ...
LITAK Tadeusz Michal
litak@...
Nov 30, 2003 9:48 am
189
... A. (2') does not imply (2) for arbitrary (bounded, distributive) lattices, but B. (2') does imply (2) for arbitrary Heyting algebras. For A, let L be the...
... A complete Heyting algebra L is also known as a locale, or frame (see, eg, P. Johnstone, Stone Spaces, CUP, 1982), and can be regarded as a generalized...
Pedro Resende
pmr@...
Nov 30, 2003 10:47 pm
191
Dear Tadeusz, Do you have references for Esakia's proof of the result you mentioned (i.e. that if in a complete Heyting algebra every element is a join of ...
Steve Vickers
s.j.vickers@...
Dec 1, 2003 10:16 am
192
Dear Professor Vickers, I'm very obliged for your e-mail, for prof. Kearnes' lucid answer (btw, is this theorem a part of the folklore or can it be attributed...
LITAK Tadeusz Michal
litak@...
Dec 4, 2003 6:56 am
193
I just noticed that the book The Structure of Finite Algebras, David Hobby and and Ralph McKenzie, American Mathematical Society, 1988, 209 pp. is among those...
Enter your vote today! A new poll has been created for the univalg group: What are your feelings about whether the value of the list would be improved by ...
univalg@yahoogroups.com
Jan 6, 2004 7:53 pm
195
Hi everyone, I resolved for 2004 to find out how people feel about having more computer scientists on the list. Note that there already are some; they are...
Hello, Autometrizable algebras, especially particular ones like MV-algebras are well-known in the literature. But the connection of the 'autometric' with...
Since I'm one of the current computer science subscribers (though my PhD was in algebra), I thought I ought to comment. I haven't voted - my mastery of...
S Vickers
s.j.vickers@...
Jan 8, 2004 7:57 pm
198
This is probably a very naive question, but ... There is a well-known correspondence between Boolean algebras and Boolean rings, that is, starting from one of...
... The problem is that axioms that ring theorists feel comfortable with tend to force booleanness. The standard translation is that + is xor (which I shall...
S Vickers
s.j.vickers@...
Jan 30, 2004 11:14 pm
200
S. Vickers: ``But unfortunately, associativity of this forces the double negation law and hence Booleanness. For'' There is a heavily studied category of...
My thanks to Steve Vickers for the detailed reply to my query. I had not considered the dual approach; the difficulties there seem clear. Let me focus on the...
... I should have been more careful. These are not neorings. In fact, I think I can show that if the + operation ( #'' in this case) gives a loop structure,...
... Any Heyting algebra with an underlying loop (or quasigroup) structure must be Boolean. For if H is a Heyting algebra that is not Boolean, then a ...
By examining the operations on {0,a,1} that commute with the retraction r, one can show that there are exactly 4 sets of operations {x+y, x*y, -x, 0, 1} such...
Thanks to Keith Kearnes for the replies ... ... Thanks. I don't know why I didn't think of trying a 3-element Heyting algebra before playing with this. ... ...
The following univalg poll is now closed. Here are the final results: POLL QUESTION: What are your feelings about whether the value of the list would be...
univalg@yahoogroups.com
Feb 1, 2004 9:11 am
207
... Yes, in my experience that seems to be widely understood as standard. ... Yes, it is. One scenic route to this is via category theory. A Heyting algebra is...
S Vickers
s.j.vickers@...
Feb 1, 2004 3:14 pm
208
... Oh, good, then I can say this. :) The replies to Michael Kinyon's interesting question, can Heyting algebras be viewed as some sort of ring the way...
Vaughan Pratt
pratt@...
Feb 1, 2004 10:33 pm
209
I don't want to write too much in followup to Vaughan, in case I digress too far from the spirit of the original question. But just to encourage those who do...
Steve Vickers
s.j.vickers@...
Feb 2, 2004 10:55 am
210
... Yes, it occurred to me after posting my message that I should have mentioned that n-ary operations need to be defined on tensor powers when they are to be...
Vaughan Pratt
pratt@...
Feb 2, 2004 11:46 pm
211
(Please, excuse for possibly multiple mail) AAA68 FIRST ANNOUNCEMENT {}From June 10 to June 13, 2004, the Institute of Algebra at Dresden University of...
R.Poe
poeschel@...
Feb 20, 2004 2:26 pm
212
This is a question from a colleague of mine who is a number theorist. ... Kathy -- ****************************************************** Katherine J. Thom...
Kathy Johnston Thom
thomk@...
Feb 23, 2004 5:07 pm
213
Looking at the book "Multuplicative Ideal Theory by R. Gilmer (Marcel Dekker 1972) will surely help to answer your questions Melvin Henriksen...
few months before someone introduced me a web site by just signing up i have received $10 and now i am getting about $1400 per month just doing nothing with no...
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