Is there a standard naming convention for set variables? Is there a standard naming convention for variables that resemble sets? Because I want to name my variables so that reading becomes as easy and intuitive as possible.
Details
Currently, I'm overlining letters: I have $\mathit{S} \in M$ and $\mathbb{T} \in N$ ($M$ and $N$ are completely different sets, having nothing to do with each other) throughout my thesis, so I find it intuitive (and think I have seen it elsewhere) to use $\overline{\mathit{S}} \in 2^M, \overline{\mathbb{T}} \in 2^N$ and then $\mathit{S} \in \overline{\mathit{S}}$.
That way, I have a strong connection between $\mathit{S}$ and $\overline{\mathit{S}}$ and can use this notation for all kind of symbols (e.g. $\mathit{S}$ as well as $\mathbb{T}$).
I like this since it is consistent. But if I'm using both $\mathit{S}$ and $\overline{\mathit{S}}$ in one definition/lemma/..., I find it unintuitive because I tend to think that $\overline{\mathit{S}}$ is the value of $\mathit{S}$ under some function.
So: Is my use of $\overline$ standard notation? Do you know of another standard? or more intuitive notation?
Update
Since $\overline$ has so many meanings already, what do you think about the following?


*

*$\ddot{\mathit{S}}$, or 

*$\overbrace{\mathit{S}}$ (which looks less strange via pdflatex), or 

*$_{2}\!\mathit{S}$

 A: My advice to you is to get your advice from your advisor. I presume that you have one, if you are writing a thesis. It is best to stick to the conventions others have set (unless they are particularly terrible). Surely your thesis cites papers, and builds on others' work. See how they denote the variables that you are after and use that convention without worrying too much.
The general convention I am familiar with is that objects get small letters ($x,y,m,n,k$), sets get capital letters ($A,B,C,X,Y$), sets of sets get calligraphic letters ($\cal U,F,M,N$), and sets of sets of sets get cursive letters ($\scr G,F,M,P$). Special sets get denoted by blackboard bold ($\Bbb{R, N, Q}$ and when context demands it, $\Bbb P$ for example).
A: If you're using $M$ as a type (i.e. writing $S \in M$ to tell us what type of object $S$ is), then any subset of $M$ is also a type. So, it would not be unreasonable to write variables denoting subsets of $M$ in the same style as $M$. If necessary, you could make a conventional choice of letter for subset variables, so that they can be easily recognized.
