Geodesic
Constructive and Non-Constructive Infinite Formulas in Computable Structures
Algebra i logika, Tome 42 (2003) no. 4, pp. 391-412.

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A transition from arbitrary $L_{\omega_1\omega}$-formulas to computable formulas in the class of computable structures is considered. It is shown that transition of a certain type is possible which doubles the complexity of the formulas. In addition, the complexity jump is analyzed for the transition from an arbitrary Scott family consisting of $L_{\omega_1\omega}$-formulas to a computable Scott family in a fixed computable structure. Exact estimates of this jump are found.
Keywords: computable structure, computable formula, Scott family. 
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P. E. Alaev. Constructive and Non-Constructive Infinite Formulas in Computable Structures. Algebra i logika, Tome 42 (2003) no. 4, pp. 391-412. http://geodesic.mathdoc.fr/item/AL_2003_42_4_a0/

[1] C. J. Ash, “Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees”, Trans. Am. Math. Soc., 298:2 (1986), 497–514 | DOI | MR | Zbl

[2] C. J. Ash, “Categoricity in hyperarithmetical degrees”, Ann. Pure Appl. Logic, 34:1 (1987), 1–14 | DOI | MR | Zbl

[3] C. J. Ash, J. F. Knight, “Relatively recursive expansions”, Fundam. Math., 140:2 (1992), 137–155 | MR | Zbl

[4] C. J. Ash, J. F. Knight, Computable structures and the hyperarithmetical hierarchy, Elsevier Science B.V., Amsterdam a. o., 2000 | MR

[5] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR