Thanks a lot for your remarks. Below my comments:

On Saturday, October 19, 2019 at 6:11:36 PM UTC+2, Benoit wrote:
>
> Not an answer, but a few remarks:
>
> * The need for more than 26 variables may be a symptom of another problem 
> than notation.  Can you give an example of a statement where you need them ?
>
The number of available variables is not the problem (within a single 
theorem). I try to use the same variable for the same concept for related 
theorems, and that is currently difficult.

>
> * A common habit in math is to name variables with primes or indices, e.g. 
> A' , A'' , A0 (displayed $A_0$), A1 etc.  Looks like someone already did 
> that (see us2.metamath.org/mpeuni/mmascii.html).
>
Great, I didn't notice that there is already an approach in my intended 
direction. We should proceed with this, as David also proposed. I thought 
about maring the alternative variables by a bar above the letter, but 
primes or indices will also do. Considering primes, however, I am afraid 
that they can be confused with the accent grave used for function values, 
e.g. ( F' ` x' ). 

>
> * You write you prefer lower case to denote terms which are always sets, 
> but I prefer to use the above "decorations" (primes and indices) to stay 
> closer to other class variables.  And also: there is a confusion which was 
> encouraged by the choice of words "set / class" for the types.  I insisted 
> to change this, and now it is " setvar / class" (already better, but I had 
> proposed "var / class" to really stop this confusion).  The real 
> distinction is "variable versus term" (in Mario's metamath 0, this is "pure 
> versus strict").
>
I completely agree. 

>
> * Finally, I see in your mm-comments "Usually used for representing a..." 
> but this is not enforceable and I think it is illusory to want future 
> contributors (human or computer ones) to use $M$ for a matrix or $P$ for a 
> polynomial, etc.
>
Maybe we should not prescribe/restrict the usage at the place where the new 
variables are defined, but we can provide conventions which variables to 
use for which concept for a special topic, e.g. "If ` A = ( N Mat R ) ` is 
the algebra of N x N matrices over (a ring) ` R ` and ` B = ( Base ` A ) ` 
is its base set (i.e. the set of all N x N matrices over ` R ` ), then 
special N x N matrix over ` R ` (i.e. elements of ` B ` ) should be denoted 
by `M ` ,  ` M' ` , ` M" ` , ` M0 ` or ` M1' `.  

>
> Benoit
>

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