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normal (ordinal) function
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(Definition)
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Definition 1 A function $F\colon\On\to\On$ is continuous if and only if for each $u\subset\On$ such that $u\neq\emptyset$ it holds that $F(\sup(u))=\sup\{F(\alpha)|\alpha\in u\}$ .
Definition 2 A function $F\colon\On\to\On$ is order preserving if and only if for each $\alpha,\beta\in\On$ such that $\alpha<\beta$ it follows that $F(\alpha)<F(\beta)$ .
Definition 3 A function $F\colon\On\to\On$ is a normal function if and only if $F$ is continuous and order preserving.
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"normal (ordinal) function" is owned by florisje.
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(view preamble | get metadata)
| Also defines: |
continuous (for ordinal functions), order preserving (for ordinal functions), normality, normal function |
| Keywords: |
ordinals, ordinal arithmetic, order preserving, continuous, normal function, normal, normality |
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Cross-references: normal, order, continuous, function
There are 2 references to this entry.
This is version 4 of normal (ordinal) function, born on 2005-10-28, modified 2005-10-29.
Object id is 7451, canonical name is NormalOrdinalFunction.
Accessed 4507 times total.
Classification:
| AMS MSC: | 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers) |
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Pending Errata and Addenda
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