Properties of Class of All Ordinals/Zero is Ordinal
Jump to navigation Jump to search
Let $\On$ denote the class of all ordinals.
We have the result that Class of All Ordinals is Minimally Superinductive over Successor Mapping.
Hence, by definition of superinductive class:
- $\O \in \On$
- $0 := \O$
and the result follows.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers: Theorem $1.2 \ (1)$