Order Automorphism on Well-Ordered Class is Forward Moving/Linguistic Note
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Linguistic Note on Order Automorphism on Well-Ordered Class is Forward Moving
The term forward moving was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$.
As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.
The concept is introduced by Raymond M. Smullyan and Melvin Fitting briefly in their Set Theory and the Continuum Problem, revised ed. of $2010$ as a stepping-stone to the stronger result Order Automorphism on Well-Ordered Class is Identity Mapping.
They do not actually give a name to the concept, but merely characterise it as a class mapping under which no element moves backwards.
It is worth comparing with the concept of a progressing mapping.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $6$: Order Isomorphism and Transfinite Recursion: $\S 2$ Isomorphisms of well orderings: Theorem $2.1$