Hi all, I have a question which looks easy, but I haven't been able to get an answer. Suppose that $L$ is a finite lattice, and that $\omega$ is the first ...
Dear Peter, It seems to me that this is essentially the same argument that says that the free object on $n$ generators in the variety generated by $L $ is the...
Friedrich Wehrung
wehrung@...
Jan 29, 2008 11:45 am
482
I think this is easy. Let k = |L|. For f_1,...,f_n in L^{omega}, let p be the function defined on omega with p(i)=(f_a(i),...,f_n(i)). There are at most k^n...
Mckenzie, Ralph N
mckenzie@...
Jan 30, 2008 9:11 pm
483
Call for Ph.D. students and postdocs -- TCS group at Univ. Pompeu Fabra The newly constituted Theoretical Computer Science (TCS) group at the Universitat...
You are cordially invited to the 46th Summer School on General Algebra and Ordered Sets. The summer school will take place in the city of Trest located 150 km...
Hello, Reforming the Calculus Class, Permanently Calculus has been the subject of immense amounts of educational material, ranging from textbooks to blog posts...
CONFERENCE ANNOUNCEMENT You are invited to participate in BLAST 2008 August 6 - 10, 2008, University of Denver, CO, USA B - Boolean Algebra L - Lattice Theory ...
Unfortunately BLAST 2008 clashes with my other obligations. My answer has to be: - I do not plan to attend, but keep me in the mailing list. best wishes A....
I find this CONFERENCE ANNOUNCEMENT very confusing to try toanswer, but here is a try at answering it. I do not plan to attend, but keep me in the mailing...
Dear people, What could be said about groups which are generated by a free semigroup? I know from the literature that they constitute a quite big class of...
Dear colleagues, Jaroslav Jezek has posted this week his collected lecture notes on universal algebra courses he held over the period of last 30 years or so....
We have a year of mathematics here (http://www.jahr-der-mathematik.de/) and so we think more often about it. Thus I'd like to ask a question: Consider...
A question for the lattice theorists: is it known if the quasi-variety of balanced lattices with 0 is actually a variety? [Using ^ for meet and v for join, a...
... It is not a variety. If you add a new zero element to any lattice L with zero it becomes balanced, and L is a quotient of this new balanced lattice. Thus,...
... Oh, right. In fact, you even answered my next question, which was about the variety generated by balanced lattices. Yes, of course. I was just being dense....
The message below was sent by Boris Schein. ... Every equivalence relation is a quasi-order (= reflexive and anti-symmetric relation). Every lattice is...
... That's a good one, alright. But since, as I understand it, the quasivariety in question cannot be finitely axiomatized in first order axioms, automated...
OK, here's another one: for each positive integer n, denote by Part (n) the partition lattice of an n-element set (e.g., the lattice of all equivalence...
Friedrich Wehrung
wehrung@...
May 6, 2008 9:38 am
500
Thank you for the lot of input. I am now trying to understand the(se) varieties. JD http://www.cococo.de...
Call A < B a subalgebra gap when A is a maximal proper subalgebra of B. The respective varieties generated by A and B need not form a variety gap V(A) < V(B),...
Vaughan Pratt
pratt@...
May 12, 2008 12:31 am
502
Jonsson¹s lemma is an obvious tool to use here. The varieties generated by the finite Heyting chains are distinct since, by Jobsson, the SIs in Var(n) are...
Brian Davey
B.Davey@...
May 12, 2008 12:37 am
503
Thanks, Brian. Meanwhile I see from Exercise 4.48(18) of MMT that every HA with a gap at the top (1 covering a penultimate b) is SI. So presumably the other...
Vaughan Pratt
pratt@...
May 12, 2008 7:18 am
504
Hi All, This is the answer to the second question by Vaughan: The three-element semigroup S consisting of a two-element left-zero semigroup with additional...
... This is false for the case when A and B are semigroups. Here is an interesting pair. Let B2 = <c,d:cc=dd=0,cdc=c,dcd=d> be the Brandt semigroup of order...
Hello everyone, I have a small problem of pedagogical nature. Is there a simple example of an infinite lattice generated by 3 elements? Of course, free lattice...
Dear Gejza, I try to attach a pdf file of an easily describable, planar, infinite lattice. It is generated by the three elements a,b,c of the picture. If...
Friedrich Wehrung
wehrung@...
May 27, 2008 11:08 am
508
Gejza , The best known easy example is called the herringbone. There is a finite version of it on page 61 of the my text ³Introduction to Lattices and ...
Brian Davey
B.Davey@...
May 27, 2008 11:18 am
509
Gejza & all, Here's an interesting pair of examples: Let A, B, C, and D be the following closed line segments in the real plane: A is the segment with...
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