Definition:Slowly Progressing Mapping

Definition

Let $C$ be a class.

Let $g: C \to C$ be a progressing mapping from $C$ to $C$.

Then $g$ is slowly progressing if and only if:

$\forall x \in \Dom g: \card {\map g x} - \card x \le 1$

That is, for all $x$ in the domain of $g$, the set $\map g x$ has at most $1$ more element than $x$ does.

Also see

• Results about slowly progressing mappings can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 9$ Supplement -- optional
• 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 $\text I$ -- Superinduction and Well Ordering: $\S 4$ Well ordering and choice: Definition $4.2$