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Zap. Nauchn. Sem. LOMI, 1976, Volume 60, Pages 183–193 (Mi znsl2077)  

Hierarchies of operators in constructive metric spaces

S. V. Pakhomov


Abstract: Infinite hierarchies of operators in constructive metric spaces (CMS's) are constructed, based on the convergence of an approximate representation of the operators. Under fairly general restrictions on the CMS (these restrictions are satisfied by, e.g., a CMS of constructive real numbers and a CMS of general recursive functions) it is shown that these hierarchies are nondegenerate. The hierarchies constructed are used for studying the complexity of operators on general recursive functions. Operators of superposition and bounded and unbounded minimization are considered, along with diverse recursion operators.

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English version:
Journal of Soviet Mathematics, 1980, 14:5, 1547–1554

Bibliographic databases:

UDC: 518.5

Citation: S. V. Pakhomov, “Hierarchies of operators in constructive metric spaces”, Studies in constructive mathematics and mathematical logic. Part VII, Zap. Nauchn. Sem. LOMI, 60, "Nauka", Leningrad. Otdel., Leningrad, 1976, 183–193; J. Soviet Math., 14:5 (1980), 1547–1554

Citation in format AMSBIB
\Bibitem{Pak76}
\by S.~V.~Pakhomov
\paper Hierarchies of operators in constructive metric spaces
\inbook Studies in constructive mathematics and mathematical logic. Part~VII
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 60
\pages 183--193
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2077}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=505352}
\zmath{https://zbmath.org/?q=an:0449.03063|0338.02016}
\transl
\jour J. Soviet Math.
\yr 1980
\vol 14
\issue 5
\pages 1547--1554
\crossref{https://doi.org/10.1007/BF01693985}


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