Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 60-66
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N. K. Kossovski. On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 60-66. http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/
@article{ZNSL_1971_20_a6,
author = {N. K. Kossovski},
title = {On algorithmical sequences belonging to the initial class of {Grzegorczyk} hierarchy},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {60--66},
year = {1971},
volume = {20},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/}
}
TY - JOUR
AU - N. K. Kossovski
TI - On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1971
SP - 60
EP - 66
VL - 20
UR - http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/
LA - ru
ID - ZNSL_1971_20_a6
ER -
%0 Journal Article
%A N. K. Kossovski
%T On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy
%J Zapiski Nauchnykh Seminarov POMI
%D 1971
%P 60-66
%V 20
%U http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/
%G ru
%F ZNSL_1971_20_a6
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 $E^0$.
