Definition:G-Set

Definition

Let $A$ be a class.

Let $g: A \to A$ be a mapping.

We say that

$x$ is a $g$-set

if and only if:

$x$ is an element of every class that is superinductive under $g$.

Also see

• Results about $g$-sets can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text {III}$ -- The existence of minimally superinductive classes: $\S 7$ Cowen's theorem