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Non-uniform autostability of models. (Russian) Zbl 0659.03011
All known stability criteria for constructivizable models give examples only of “uniformly” autostable models: for any such model A there exists an effective procedure p(x,y,z) such that for any computable sequence $$\pi =(\mu_ 0,\mu_ 1,...)$$ of constructivizations of A, any $$\mu_ i$$, $$\mu_ j\in \pi$$ and suitable finite mapping $$\alpha_ m$$, p(i,j,m) is a number of a recursive function that extends $$\alpha_ m$$ to a reduction of $$\mu_ i$$ to $$\mu_ j$$. The author gives a modification of S. S. Goncharov’s method [Algebra Logika 19, 507- 551 (1980; Zbl 0514.03029)] and constructs an example of a non-uniformly autostable model. Thus he establishes that the Goncharov’s sufficient criterion for autostability is not necessary.
Reviewer: S.R.Kogalovskij

MSC:
 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures
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