Ordinal notation system: Difference between revisions
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- [[Pair sequence system]] |
- [[Pair sequence system]] |
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- Ordinal notation systems associated to [[ordinal collapsing functions]] |
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- [[Taranovsky's ordinal notations]] |
- [[Taranovsky's ordinal notations]] (the ones that are well-ordered) |
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- [[Patterns of resemblance]] |
- [[Patterns of resemblance]] |
Revision as of 17:40, 11 July 2023
An ordinal notation system (also called an ordinal notation informally) is a system of names for ordinals, or equivalently, a well-ordered set of objects that "can be considered names". There may not be a formal restriction of what objects can be considered names, but most common examples include strings, sequences, trees/hydras, and terms built up from constants and functions. Most authors also require the well-order to be recursive, and this requirement is included in the definition of proof-theoretic ordinals that uses ordinal notation systems.
Notable ordinal notation systems include:
- Ordinal notation systems associated to ordinal collapsing functions
- Taranovsky's ordinal notations (the ones that are well-ordered)
- Y sequence (as long as it is well-ordered)