Definition:Well-Ordered Class under Subset Relation
Jump to navigation
Jump to search
Definition
Let $A$ be a class which is also a nest.
Let $A$ have the property that every non-empty subclass of $A$ has a smallest element under the subset relation.
Then $A$ is said to be well-ordered under the subset relation.
Also known as
Some sources refer to the subset relation as the inclusion relation, and so the name of this property becomes well-ordered under inclusion.
Sources
- 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 $4.8$