Geodesic
On maximal subalgebras of the algebras of unary recursive functions
Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 3, pp. 81-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the algebras of unary functions with supports in countable primitively recursively closed classes and composition operation. Each algebra of this type is proved to have continuum many maximal subalgebras including the set of all unary functions of the class $\mathcal E^2$ of the Grzegorczyk hierarchy. Bibliogr. 13.
Mots-clés : maximal subalgebra
Keywords: unary recursive function. 
@article{DA_2016_23_3_a4,
     author = {S. S. Marchenkov},
     title = {On maximal subalgebras of the algebras of unary recursive functions},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {81--92},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2016_23_3_a4/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - On maximal subalgebras of the algebras of unary recursive functions
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2016
SP  - 81
EP  - 92
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2016_23_3_a4/
LA  - ru
ID  - DA_2016_23_3_a4
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T On maximal subalgebras of the algebras of unary recursive functions
%J Diskretnyj analiz i issledovanie operacij
%D 2016
%P 81-92
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2016_23_3_a4/
%G ru
%F DA_2016_23_3_a4
S. S. Marchenkov. On maximal subalgebras of the algebras of unary recursive functions. Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 3, pp. 81-92. http://geodesic.mathdoc.fr/item/DA_2016_23_3_a4/

[1] S. A. Berezin, “An algebra of unate primitive recursive functions with iteration operation of general form”, Cybern., 12:3 (1976), 346–353 | DOI | MR | Zbl

[2] S. A. Berezin, “Maximal subalgebras of recursive function algebras”, Cybern., 14:6 (1978), 935–938 | DOI | MR | Zbl

[3] G. P. Gavrilov, “On functional completeness in a countable-valued logic”, Problems of Cybernetics, 15, ed. A. A. Lyapunov, Nauka, Moscow, 1965, 5–64 | MR | Zbl

[4] A. Grzegorczyk, Some classes of recursive functions, v. 4, Mathematical Apparatus, Pol. Tow. Mat., Warsaw, 1953 | MR | MR

[5] V. V. Koz'minykh, “On primitive recursive functions of a single argument”, Algebra Logic, 7:1 (1968), 44–53 | DOI | MR

[6] S. S. Marchenkov, “A method for constructing maximal subalgebras of algebras of general recursive functions”, Algebra Logic, 17:5 (1978), 383–392 | DOI | MR

[7] S. S. Marchenkov, “On cardinality of the set of precomplete classes in some classes of a countable-valued logic”, Problems of Cybernetics, 38, ed. S. V. Yablonskii, Nauka, Moscow, 1981, 109–116 | MR | Zbl

[8] S. S. Marchenkov, Elementary Recursive Functions, MTsNMO, Moscow, 2003

[9] S. S. Marchenkov, Functional Systems with Superposition Operation, FIZMATLIT, Moscow, 2004 | MR

[10] V. L. Mikheev, “Class of algebras of primitive recursive functions”, Math. Notes Acad. Sci. USSR, 14:1 (1981), 638–645 | DOI | MR | Zbl

[11] R. W. Ritchie, “Classes of predictably computable functions”, Trans. Amer. Math. Soc., 106:1 (1963), 139–173 | DOI | MR | MR | Zbl

[12] M. G. Rozinas, “An algebra of many-placed primitive recursive functions”, Scientific Notes of Ivanovo State Pedagogical Institute, 117, ISPI, Ivanovo, 1972, 95–111

[13] V. A. Sokolov, “Maximal subalgebras of the algebra of all partially recursive functions”, Cybern., 8:1 (1972), 76–79 | DOI | MR | Zbl