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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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