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- Kleene's_O abstract "In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations. It contains ordinal notations for every recursive ordinal, that is, ordinals below Church–Kleene ordinal, . Since is the first ordinal not representable in a computable system of ordinal notations the elements of can be regarded as the canonical ordinal notations. Kleene (1938) described a system of notation for all recursive ordinals (those less than the Church–Kleene ordinal). It uses a subset of the natural numbers instead of finite strings of symbols. Unfortunately, there is in general no effective way to tell whether some natural number represents an ordinal, or whether two numbers represent the same ordinal. However, one can effectively find notations which represent the ordinal sum, product, and power (see ordinal arithmetic) of any two given notations in Kleene's and given any notation for an ordinal, there is a recursively enumerable set of notations which contains one element for each smaller ordinal and is effectively ordered.".
- Kleene's_O wikiPageExternalLink S0002-9904-1938-06720-1.
- Kleene's_O wikiPageID "16105044".
- Kleene's_O wikiPageRevisionID "567806263".
- Kleene's_O hasPhotoCollection Kleene's_O.
- Kleene's_O subject Category:Ordinal_numbers.
- Kleene's_O type Abstraction100002137.
- Kleene's_O type DefiniteQuantity113576101.
- Kleene's_O type Measure100033615.
- Kleene's_O type Number113582013.
- Kleene's_O type OrdinalNumber113597280.
- Kleene's_O type OrdinalNumbers.
- Kleene's_O comment "In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations. It contains ordinal notations for every recursive ordinal, that is, ordinals below Church–Kleene ordinal, . Since is the first ordinal not representable in a computable system of ordinal notations the elements of can be regarded as the canonical ordinal notations.".
- Kleene's_O label "Kleene's O".
- Kleene's_O sameAs m.03qp7k0.
- Kleene's_O sameAs Q6420083.
- Kleene's_O sameAs Q6420083.
- Kleene's_O sameAs Kleene's_O.
- Kleene's_O wasDerivedFrom Kleene's_O?oldid=567806263.
- Kleene's_O isPrimaryTopicOf Kleene's_O.