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Let $C$ be a class.
Let $f: C \to C$ be a mapping from $C$ to $C$.
Then $f$ is inflationary if and only if:
- $x \in C \implies x \subseteq \map f x$
An inflationary mapping is also known as a progressive mapping or progressing mapping.
Some sources use progressing function.
- Results about inflationary mappings can be found here.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.4$