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Zap. Nauchn. Sem. LOMI, 1972, Volume 32, Pages 105–107 (Mi znsl2571)  

Some properties of graphs of functions in the Grzegorczyk hierarchy

S. V. Pakhomov


Abstract: Let $\Gamma^n$ be the set of all primitive recursive functions whose graphs belong to $\varepsilon^n$ [I]. It is proved that $\Gamma^n$ is the closure of $\varepsilon^n$ relative to identification and permutation of variables, to substitution of constants and to special operations I)–4) on p.p. 105–106. In particular $f_n\in\Gamma^0$ for every $n\geq 3$. Here $f_n$ is a modification of Ackermana's function described in [I] p. 30.

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Citation: S. V. Pakhomov, “Some properties of graphs of functions in the Grzegorczyk hierarchy”, Studies in constructive mathematics and mathematical logic. Part V, Zap. Nauchn. Sem. LOMI, 32, "Nauka", Leningrad. Otdel., Leningrad, 1972, 105–107

Citation in format AMSBIB
\Bibitem{Pak72}
\by S.~V.~Pakhomov
\paper Some properties of graphs of functions in the Grzegorczyk hierarchy
\inbook Studies in constructive mathematics and mathematical logic. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1972
\vol 32
\pages 105--107
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2571}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=332461}


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