Dear Members, When trying to switch from a deep to a shallow embedding of a system into the rigidly-typed logic of a theorem prover, I discovered that I need...
Andrei, This is Birkhoff's completeness theorem for equational logic. See Theorem 2 on page 170 of G. Gratzer's "Universal Algebra", 2nd edition. (See also...
Brian Davey
B.Davey@...
Jun 4, 2008 12:22 am
528
Brian, Do you know that my book is again available? GG...
Dear George, Can your UA book be ordered now? (Springer?) Fred ... Dear George, Can your UA book be ordered now? (Springer?) Fred Le 4 juin 08 à 04:23, George...
Friedrich Wehrung
wehrung@...
Jun 4, 2008 8:35 am
530
Dear Fred, I have not tried, but I assume so. GG ... Dear Fred, I have not tried, but I assume so. GG On 4-Jun-08, at 3:35 AM, Friedrich Wehrung wrote: Dear...
I checked on amazon.com. There, the paperback version can be pre-ordered. Is there a hard copy version available? Matt Insall From: univalg@yahoogroups.com...
I called the publisher. It slipped from June to mid July. GG ... I called the publisher. It slipped from June to mid July. GG On 4-Jun-08, at 9:30 AM, Insall,...
Hello Andrei, i) Why do you need the same cardinality with alphabet and function symbols? ii) From syntactical equivalence folows semantical equivalence in the...
Dear Brian and Jens, I thank you very late for your answers since I had been expecting to receive all potential answers on my email account and have not...
I wonder how the Birkhoff completeness theorem complies with Goedel's incompleteness theorem. If we have arithmetic formulas, which are neither provable nor...
Jens, As far as I know, Godel's (first) incompleteness theorem implies (or, rather, has as an instance the fact) that the set of first-oder sentences satisfied...
Hello Andrei, consider a grammar G, which generates terms T and also consider equations E out of language L(G), which together with G define a terminating and...
Dear Andrei, ... counterexample: take a signature with countably many constants and uncountably many unary function symbols, and let X be countable. Then...
Till Mossakowski
till@...
Jun 25, 2008 8:04 am
539
Dear Jens, Canonic (i.e., confluent and terminating) TRS's indeed provide a decision procedure for their corresponding equational theories. Yet these...
Dear Till, Many thanks for your answer and it is nice to hear from you! Your example indeed shows that I cannot get away with the classical proof ``up to...
Hello Andrei, thanks for answer and the keywords. I did a search for "equational theory" on http://citeseer.ist.psu.edu/ and found some seemingly useful...
Dear fellow members Im interested in RECENT work that has been done in the area of factorization of algebraic structures. Ie. Unique factorization properties,...
While on a committee for a graduation paper I ran into an incorrect proof of the following theorem: Let a_1 \geq a_2\geq ... \geq a_n >0 be integers. Then the...
I just realized that the answer to my question is obvious, the auxiliary result is trivial to prove. I should have thought about it before posting. Sorry. ...
Hello list, when reasoning about real numbers I came across quadratic fields and the proof for "sqrt(2) is irrational". The proof is fully algebraic and I do...
A book I'm currently reading, "the Beginnings & Evolution of Algebra" (Bashmakova and Smirnova, published by the MAA) notes that the construction of the cube...
Dear colleagues, I just received the following question from a model-theoretical colleague of mine. For simplicity, I translate it to the language of varieties...
Friedrich Wehrung
wehrung@...
Sep 12, 2008 2:56 pm
549
Fred- Can you clarify this part? ... Do you mean "equations" or "variables"? -- Keith A. Kearnes Email: kearnes@... Department of...
I mean "equations"---so, k is infinite (otherwise the question wouldn't make much sense). So, A is k-equationally compact iff for any system $\Sigma$ of less...
Friedrich Wehrung
wehrung@...
Sep 12, 2008 3:11 pm
551
Good morning Friedrich, does "finitly solvable" mean a) finitly many solutions b) solvable in a finite variety and are these proper algebras for your theorem: ...
Hi Jens, An equation system S is "finitely solvable" in an algebra A, if every finite subsystem of S has a solution in A. Positive example: any vector space V...
Friedrich Wehrung
wehrung@...
Sep 17, 2008 7:56 am
553
What is known about varieties with a ternary term t(x,y,z) (which I'll abbreviate here to xyz) satisfying (vwx)yz = v(wxy)z = vw(xyz)? (Hence all terms built...
Vaughan Pratt
pratt@...
Sep 20, 2008 5:49 am
554
Dear Vaughan, Are you really asking what you want to ask? (Since my question sounds funny, I am writing only to you, not to the mailing list) The affine things...
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