Definition:Universal Class

Definition
The universal class is the class of which all sets are members.

The universal class is defined most commonly in literature as:


 * $V = \set {x: x = x}$

where $x$ ranges over all sets.

It can be briefly defined as the class of all sets.

Notation
The use of $V$ as the symbol used to denote the universal class follows the presentation by and, in their.

Much of the literature uses $U$ and its variants, for example $\Bbb U$.

However, as $U$ is often used to denote the universal set, prefers to use $V$ for the universal class in order to reduce confusion between the two.

The symbol $\mathfrak A$ is also seen in older literature; however, the number of those who still like using this awkward and difficult-to-read Germanic font is decreasing.

Also see

 * Definition:Universal Set


 * Definition:Model of Class-Set Theory


 * Fundamental Law of Universal Class