On computable enumerations. I. (English. Russian original) Zbl 0273.02024
Algebra Logic 7(1968), No. 5, 330-346 (1969); translation from Algebra Logika 7, No. 5, 71-99 (1968).
MSC:
| 03D20 | Recursive functions and relations, subrecursive hierarchies |
| 03D25 | Recursively (computably) enumerable sets and degrees |
| 03D99 | Computability and recursion theory |
References:
| [1] | Yu. L. Ershov, ”Enumerations of familes of general recursive functions,” Sibirsk. Matem. Zh.,8, No. 5, 1015–1025 (1967). |
| [2] | Yu. L. Ershov, ”On a hierarchy of sets I, II,” Algebra i Logika,7, No. 1, 47–74 (1968);7, No. 4, 15–47 (1968). · Zbl 0216.00901 |
| [3] | A. I. Mal’tsev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965). |
| [4] | A. I. Mal’tsev, ”Complete enumerable sets,” Algebra i Logika,2, No. 2, 4–30 (1963). |
| [5] | A. I. Mal’tsev, ”On the theory of computable sets of objects,” Algebra i Logika,3, No. 4, 5–31 (1965). |
| [6] | A. I. Mal’tsev, ”Positive and negative enumerations,” Dokl. Akad. Nauk SSSR,160, No. 2, 278–280 (1965). |
| [7] | A. A. Muchnik, ”Isomorphism systems of recursive denumerable sets with effective properties,” Trudy Mosk. Matem. Obsh-va,7, 407–412 (1958). |
| [8] | V. A. Uspenskii, ”Systems of denumerable sets and their enumerations,” Dokl. Akad. Nauk SSSR,105, No. 6, 1155–1158 (1955). |
| [9] | V. A. Uspenskii, Lectures on Computable Functions, Fizmatgiz (1960). |
| [10] | A. B. Khutoretskii, ”On enumerations of partial recursive functions” (in press). |
| [11] | J. P. Cleave, ”Creative functions,” Z. Math. Log. Gr. Math.,7, 205–212 (1961). · Zbl 0102.00803 · doi:10.1002/malq.19610071108 |
| [12] | R. M. Friedberg, ”Three theorems on recursive functions,” Journ. Symb. Log.,23, 309–318 (1958). · Zbl 0088.01601 · doi:10.2307/2964290 |
| [13] | A. H. Lachlan, ”Standard classes of recursively enumerable sets,” Z. Math. Log. Gr. Math.,10, 23–42 (1964). · Zbl 0282.02016 · doi:10.1002/malq.19640100203 |
| [14] | A. H. Lachlan, ”On the indexing of classes of recursively enumerable sets,” Journ. Symb. Log.,31, 10–22 (1966). · Zbl 0143.01203 · doi:10.2307/2270617 |
| [15] | J. Myhill, ”Creative sets,” Z. Math. Log. Gr. Math.,1, 23–42 (1965). |
| [16] | M. B. Pour-El, ”Gödel numberings versus Friedberg numberings,” Proc. Amer. Math. Soc.,15, No. 2, 252–255 (1964). · Zbl 0168.25404 |
| [17] | R. M. Smullian, ”Theory of formal systems,” Ann. Math. Studies (1961). |
| [18] | N. Shapiro, ”Degrees of computability,” Trans. Amer. Math. Soc.,82, 281–299 (1956). · Zbl 0070.24602 · doi:10.1090/S0002-9947-1956-0085187-3 |
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