Inner constructivizability of functional structures
Algebra i logika, Tome 61 (2022) no. 1, pp. 23-41.

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We construct and look at examples of (functional) structures the hereditarily finite superstructures over which have rank of inner constructivizability 0.
Keywords: functional structure, hereditarily finite superstructure, inner constructivizability.
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A. S. Burnistov; A. I. Stukachev. Inner constructivizability of functional structures. Algebra i logika, Tome 61 (2022) no. 1, pp. 23-41. http://geodesic.mathdoc.fr/item/AL_2022_61_1_a1/

[1] R. Montague, “Recursion theory as a branch of model theory”, Logic, Methodology Philos. Sci. III, Proc. 3rd internat. Congr. (Amsterdam, 1967), 1968, 63–86

[2] A. I. Stukachev, “O vnutrennei konstruktiviziruemosti dopustimykh mnozhestv”, Vestn. NGU, Ser. matem., mekh., inform., 5:1 (2005), 69–76

[3] A. Stukachev, “Effective model theory: an approach via $\Sigma$-definability”, Effective mathematics of the uncountable, Lect. Notes Log., 41, eds. N. Greenberg et al., Cambridge Univ. Press, Cambridge; Assoc. Symb. Log. (ASL), 2013, 164–197

[4] H. Rogers, Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967; Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972

[5] Yu. L. Ershov, Opredelimost i vychislimost, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996

[6] Y. N. Moschovakis, Elementary induction on abstract structures, Stud. Logic Found. Math., 77, North-Holland Publ. Co., Amsterdam–London; Am. Elsevier Publ. Co., New York, 1974

[7] J. Barwise, Admissible Sets and Structures, Springer-Verlag, Berlin a.o., 1975

[8] A. I. Stukachev, “Uniformization property in hereditary finite superstructures”, Sib. Adv. Math., 7:1 (1997), 123–132