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- Ordinal_notation abstract "In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language.There are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Wilfried Buchholz, Georg Cantor, Solomon Feferman, Gerhard Jäger, Isles, Pfeiffer, Wolfram Pohlers, Kurt Schütte, Gaisi Takeuti (called ordinal diagrams), Oswald Veblen. Given such a scheme, one should be able to define a recursive well-ordering of a subset of the natural numbers by associating a natural number with each finite sequence of symbols via a Gödel numbering. Stephen Cole Kleene has a system of notations, called Kleene's O, which includes ordinal notations but it is not as well behaved as the other systems described here.Usually one proceeds by defining several functions from ordinals to ordinals and representing each such function by a symbol. In many systems, such as Veblen's well known system, the functions are normal functions, that is, they are strictly increasing and continuous in at least one of their arguments, and increasing in other arguments. Another desirable property for such functions is that the value of the function is greater than each of its arguments, so that an ordinal is always being described in terms of smaller ordinals. There are several such desirable properties. Unfortunately, no one system can have all of them since they contradict each other.".
- Ordinal_notation wikiPageExternalLink ords.ps.
- Ordinal_notation wikiPageID "6108552".
- Ordinal_notation wikiPageRevisionID "489351353".
- Ordinal_notation hasPhotoCollection Ordinal_notation.
- Ordinal_notation subject Category:Mathematical_notation.
- Ordinal_notation subject Category:Ordinal_numbers.
- Ordinal_notation subject Category:Proof_theory.
- Ordinal_notation type Abstraction100002137.
- Ordinal_notation type DefiniteQuantity113576101.
- Ordinal_notation type Measure100033615.
- Ordinal_notation type Number113582013.
- Ordinal_notation type OrdinalNumber113597280.
- Ordinal_notation type OrdinalNumbers.
- Ordinal_notation comment "In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language.There are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Wilfried Buchholz, Georg Cantor, Solomon Feferman, Gerhard Jäger, Isles, Pfeiffer, Wolfram Pohlers, Kurt Schütte, Gaisi Takeuti (called ordinal diagrams), Oswald Veblen.".
- Ordinal_notation label "Ordinal notation".
- Ordinal_notation sameAs m.0fqgt1.
- Ordinal_notation sameAs Q7100790.
- Ordinal_notation sameAs Q7100790.
- Ordinal_notation sameAs Ordinal_notation.
- Ordinal_notation wasDerivedFrom Ordinal_notation?oldid=489351353.
- Ordinal_notation isPrimaryTopicOf Ordinal_notation.