Generalized computable numerations and nontrivial rogers semilattices
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We outline the general approach to the notion of a computable numeration in the frames of which computable numerations, of families of arithmetic sets are studied.
KeywordsRecursive Function Existential Quantifier Computable Numberings Algorithm Theory Recursive Model
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- 2.Yu. L. Ershov,Numeration Theory [in Russian], Nauka, Moscow (1977).Google Scholar
- 3.Yu. L. Ershov,Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).Google Scholar
- 4.A. I. Mal'tsev,Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).Google Scholar
- 5.S. C. Kleene,Introduction to Metamathematics, Princeton, N. J. (1952).Google Scholar
- 6.A. N. Kolmogorov and V. A. Uspenskii, “Defining an Algorithm,”Usp. Mat. Nauk, 13, No. 4 (82), 2–28 (1958).Google Scholar
- 7.V. A. Uspenskii, “Systems of denumerable sets and their numerations,”Dok. Akad. Nauk SSSR, 105, No. 6, 1155–1158 (1955).Google Scholar
- 8.V. A. Uspenskii,Lectures on Computable Functions [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
- 11.I. A. Lavrov, “Computable numberings,” inProc. 5th Int. Congr. Logic, Methodology and Philosophy of Science, Part 1, Reidel, Dordrecht (1977), pp. 195–206.Google Scholar
- 14.S. S. Goncharov, “The problem of the number of non-autoequivalent constructivizations,”Dokl. Akad. Nauk SSSR, 251, No. 2, 271–274 (1980).Google Scholar
- 15.A. I. Maltsev, “Toward a theory of computable families of objects,”Algebra Logika, 3, No. 4, 5–31 (1964).Google Scholar
- 17.Yu. L. Ershov,Definability and Computability [in Russian], Nauch. Kniga, Novosibirsk (1996).Google Scholar
- 18.A. B. Khutoretskii, “On the cardinality of the upper semilattice of computable numerations,”Algebra Logika, 10, No. 5, 561–569 (1971).Google Scholar
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