Abstract
A transition from arbitrary \(L_{\omega _{\text{1}} \omega }\)-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\(L_{\omega _{\text{1}} \omega }\)-formulas to a computable Scott family in a fixed computable structure. Exact estimates of this jump are found.
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