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:


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

Notation
Variants on $U$ are often seen, for example $\Bbb U$.

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

In the treatment of Von Neumann-Bernays-Gödel set theory presented by and, in their , the symbol $V$ is used, with a view to tying it in with the concept of a model of class-set theory.

Also see

 * Definition:Universal Set


 * Fundamental Law of Universal Class