Geodesic
Index Sets of Autostable Relative to Strong Constructivizations Constructive Models
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 43-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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Found complexity of Index sets of autostable relative to strong constructivizations constructive models with strong constructivizations and strong constructive models.
Keywords: computable model, decidable model, constructive model, strong constructive model, numbering, computable numberings, hyperarithmetical hierarchy, index sets, autostable models, categorical models. 
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S. S. Goncharov; M. I. Marchuk. Index Sets of Autostable Relative to Strong Constructivizations Constructive Models. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 43-67. http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a3/

[1] S. S. Goncharov, J. F. Knight, “Computable structure and non-structure theorems”, Algebra and Logic, 41:6 (2002), 351–373 | DOI | MR | Zbl

[2] A. T. Nurtazin, Computable classes and algebraic criteria autostability, Thes. Cand. Math.-Phys. Degree, Alma-Ata, 1974 (in Russian) | Zbl

[3] S. S. Goncharov, Yu. L. Ershov, Constructive Models, Kluwer Academic/Plenum Press, New York, 2002

[4] S. S. Goncharov, “Problem of the number of non-self-equivalent constructivizations”, Algebra and Logic, 19:6 (1980), 401–414 | DOI | MR

[5] Goncharov S. S., “Computability and Computable Models, Mathematical problems from applied logic, II”, Logics for the XXIst century, International Mathematical Series (New York), eds. D. M. Gabbay, S. S. Goncharov, M. Zakharyaschev, Springer, N. Y., 2006 | MR

[6] S. S. Goncharov, “Index sets almost simple constructive models”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:3 (2013), 38–52 | MR | Zbl

[7] E. B. Fokina, “Index sets of decidable models”, Sib. Mat. J., 48:5 (2007), 939–948 | DOI | MR | Zbl

[8] E. N. Pavlovskii, “Estimation of the algorithmic complexity of classes of computable models”, Sib. Mat. J., 49:3 (2008), 512–523 | DOI | MR

[9] E. N. Pavlovskii, “Index sets of simple models”, Sib. Electr. Mat. Izv., 5 (2008), 200–210 (in Russian) | MR

[10] A. T. Nurtazin, “Strong and weak constructivization and computable families”, Algebra and Logic, 13:3 (1974), 177–184 | DOI | MR | Zbl

[11] Goncharov S. S., Nurtazin A. T., “Constructive Models of Complete Solvable Theories”, Algebra Logic, 12:2 (1973), 67–77 | DOI

[12] H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Company, New York, 1967 | MR | MR | Zbl

[13] Yu. L. Ershov, E. A. Palyutin, Matematical Logic, Mir Publisher, M., 1984 | MR | Zbl

[14] Goncharov S. S., Countable Boolean Algebras and Decidability, Kluwer Academic/Plenum Publishers, N.Y., etc., 1997 | MR

[15] Peretyat'kin M. G., “Strongly Constructive Models and Numerations of the Boolean Algebra of Recursive Sets”, Algebra Logic, 10:5 (1971), 332–345 | DOI | MR

[16] Goncharov S. S., Khoussainov B., “Complexity of Categorical Theories with Computable Models”, Algebra and Logic, 43:6 (2004), 365–373 | DOI | MR | Zbl

[17] Marker D., “Non-$\Sigma_n$-Axiomatizable Almost Strongly Minimal Theories”, J. Symbolic Logic, 54:3 (1989), 921–927 | DOI | MR | Zbl