Definition:Strictly Well-Founded Relation/Definition 3
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Definition
Let $\struct {S, \RR}$ be a relational structure.
Let $\RR$ be a well-founded relation which is also antireflexive.
Then $\RR$ is a strictly well-founded relation on $S$.
Also known as
A strictly well-founded relation is also known in the literature as a foundational relation.
It is commonplace in the literature and on the internet to use the term well-founded relation for strictly well-founded relation.
However, $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers the more cumbersome and arguably more precise strictly well-founded relation in preference to all others.
Some sources do not hyphenate, and present the name as strictly wellfounded relation.
Also see
Sources
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Definition $1$