Axiom:Axiom of Transitivity

Axiom

Let $V$ be a basic universe.

$V$ is a transitive class.

That is, every set $S$ which is an element of $V$ is a subclass of $V$.

Briefly:

Every set is a class.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 2$ Transitivity and supercompleteness: $A_1$