The axiomatization of Quantity Calculus, the logical foundations of DA

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I was intrigued reading * http://en.wikipedia.org/wiki/Quantity_calculus" [Broken] that after two centuries axiomatization of QC has not been completed, though there are only 5 basic elements and 4[3] concepts:
S[tandard],= U[nit], D[imension], Q[uantity]. I suppose nobody here has tackled the problem or knows the state of the art or can tell whether the task is unnecessary or impossible, but, with your help, I would like to examine the problem.

I tried to gather basic scientific information, I found a "formal? " definition of Q http://en.wikipedia.org/wiki/Quantity" [Broken] in DA. Moreover, in the article * we read that QC... is "analogous" to a system of algebra with units instead of variables. Now, could you tell me if
1) VIM3's is the official, best definition available of Q
2) [you know or] where to find an appropriate definition of D in D[imensional] A[nalysis] and in relation to Q
3) set theory [arithmetics] ZFC is appropriate for a sistem "analogous" to algebra
4) the fact that different entities share same dimensions is an obstacle to axiomatization
5) there is a list of derived quantities
 
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question 3) is discussed in another thread
5) I know there is a list, but I can't remember where I saw it (there were some 30 items). It is not at wiki : "list of derived quantities". This question is not important
 
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