# 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
• $_{2}\!\mathit{S}$
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I don't fully understand what you mean by that. Can you give more context? What field is your thesis in? In either case, overlining is bad and it is way way overly used in mathematics. I wouldn't recommend it. – Asaf Karagila Jun 28 '13 at 15:45
Its theoretical computer science: model checking and automata theory. – DaveBall aka user750378 Jun 28 '13 at 15:47
I tend to use small letters for items, big letters for sets, \mathcal for sets of sets and \mathfrak for sets of sets of sets (e.g. $a\in A\in\mathcal{A}\in\mathfrak{A}$). – Ido Jun 28 '13 at 15:49
Because if I write $\overline A$ then one person would think this is the complement of $A$, another would think its the closure of $A$, and another may think it's a whole other thing. – Asaf Karagila Jun 28 '13 at 15:50
Actually, I had course about automata theory and overline was used to denote complement. Another common approach is to use different sequences of the alphabet for different meanings. For example, $A,B,C$ for sets and $X,Y,Z$ for sets of sets. – Ido Jun 28 '13 at 16:00

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).
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.