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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1971 Volume 20, Pages 60–66 (Mi znsl2397)

On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy

N. K. Kossovski


Abstract: It is proved that for any recursive sequence $f$ there exists a sequence $g$ of Grzegorczyk class $E^0$ such that $g(0),g(1),\dots$ is obtained from $f(0),f(1),\dots$ by replacing some members $f(i)$ by finite sequences $f(i),\dots,f(i)$.
This implies that every recursively convergent recursive sequence of rational numbers can be represented by a functions from $E^0$.



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