Definition:Small Class

Definition
Let $A$ denote an arbitrary class.

Then $A$ is said to be small iff:


 * $\exists x: x = A$

where $=$ denotes class equality and $x$ is a set variable.

That is, a class is small if and only if it is equal to some set variable.

To denote that a class $A$ is small, the notation $\mathscr M \left({A}\right)$ may be used.

Thus, $\mathscr M \left({A}\right)$ iff $\exists x: x = A$.

Remark
Small classes correspond to sets.

They are, however, distinct from set variables because set variables are arbitrarily chosen.

Also, classes are no more than definitional abbreviations in the language of set theory that enhance our expressivity.

By Set is Small Class, all set variables can be considered small classes.