Axiom:Axiom of Swelledness

Axiom

Let $V$ be a basic universe.

$V$ is a swelled class.

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

Briefly:

Every subclass of a set is a set.

Also see

• Results about the Axiom of Swelledness can be found here.

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: $A_2$