When you want to say, for example, that $a$ is an integer, you write it as $a \in \mathbb{Z}$, which is read as "$a$ is an element of the set of all integers". But, because of the notorious nonexistence of the set of all sets, you can't say something like $S \in \mathbb{S}$, where $\mathbb{S}$ is my goofy nonce-glyph for said nonexistent set. Is there any valid notational way to indicate that $S$ is a set?
If I'm writing a mathematical paper, I'll just write out "$S$ is a set" in English for the sake of clarity, but for my own notes I prefer to lean on notation as much as possible for the sake of brevity and unambiguity. Notes being notes, I do take liberties, but I'd like to adhere to standards if the standards are there.
Is it possible to quantify something as a set without simply saying, in natural language, that it is a set?