Definition:Extending Operation
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Definition
Let $S$ denote the class of all ordinal sequences.
Let $E: S \to S$ be a mapping whose behaviour is such that:
where $\alpha^+$ is the successor ordinal of $\alpha$.
Then $E$ is an extending operation.
That is, $E$ extends every ordinal sequence of length $\alpha$ to an ordinal sequence of length $\alpha^+$.
Also see
- Results about extending operations 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: $\S 5$ Transfinite recursion theorems