Algorithmic representation of wermus' constructions of ordinal numbers
In his paper [3] Wermus defines ordinal numbers as "Z - symbols" of the form [a1n ..., ak κ, ≥ 1 and [a1] , where the aj, 1≤ j, ≤ κ, are natural numbers or Z -symbols. It wi II be demonstrated that Wermus' constructions can be described by means of a special Neumer algorithm, the c...
- Autores:
-
Fuchs, Hartwig
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1971
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42189
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42189
http://bdigital.unal.edu.co/32286/
- Palabra clave:
- Wermus
ordinal numbers
natural numbers
constructive algorithm
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In his paper [3] Wermus defines ordinal numbers as "Z - symbols" of the form [a1n ..., ak κ, ≥ 1 and [a1] , where the aj, 1≤ j, ≤ κ, are natural numbers or Z -symbols. It wi II be demonstrated that Wermus' constructions can be described by means of a special Neumer algorithm, the constructive algorithm of [1], part I and V resp. a descriptive algorithm of [2], part III ; more precisely: that there can be established a 1-1 correspondence between Z- symbolsi [a1n ..., ak ] and algorithmic symbols T[a1n ..., ak ] such that [a1n ..., ak ] and T[a1n ..., ak ] represent the same ordinal number. This comparision of the two systems further allows the determination of the least ordinal number which is inaccesible by Wermus' constructions in [3]. |
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