Well-Ordered Class is not Isomorphic to Initial Segment/Also presented as
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Well-Ordered Class is not Isomorphic to Initial Segment: Also presented as
Some sources present this result in the context of well-ordered sets, and do not take into account the concept of classes.
The result is the same whether the domain of any hypothetical order isomorphism is a set or a propr class.
Sources
- 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.7$: Well-Orderings and Ordinals: Theorem $1.7.4$