Definition:Proper Well-Ordering
Jump to navigation
Jump to search
Definition
Let $V$ be a basic universe.
Let $A$ be a class.
Let $\RR$ be a well-ordering on $A$.
Then $\RR$ is a proper well-ordering if and only if:
- every proper lower section of $A$ is a set.
Also see
- Well-Ordering on Set is Proper Well-Ordering, showing that this definition is meaningful only in the context of class theory
- Results about proper well-orderings can be found here.
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: $\S 1$ A few preliminaries