Definition:Universe of Discourse

Definition
The universe of discourse, or just universe, is the term used to mean everything we are talking about.

Otherwise known as the universe of interpretation or domain of discourse.

When introducing the symbols $\forall$ (the universal quantifier) or $\exists$ (the existential quantifier), it is understood that the objects referred to are those in the specified universe. It is usual to define that universe.

Also see

 * In class theory, the universe of discourse is the Universal Class