Publicado

1971-01-01

Algorithmic representation of wermus' constructions of ordinal numbers

Palabras clave:

Wermus, ordinal numbers, natural numbers, constructive algorithm, (es)

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Autores/as

  • Hartwig Fuchs

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].