Definition:Strict Strong Well-Ordering/Linguistic Note
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Linguistic Note on Strict Strong Well-Ordering
The term Strict Strong Well-Ordering was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ to distinguish between this notion and the weaker notion of a strict well-ordering.
As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.
In the presence of the Axiom of Foundation, a strict strong well-ordering and a strict well-ordering are equivalent.