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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 5(395), Pages 107–142 (Mi umn9373)  

This article is cited in 2 scientific papers (total in 2 papers)

On autostability of almost prime models relative to strong constructivizations

S. S. Goncharov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Questions of autostability and algorithmic dimension of models go back to papers by A. I. Malcev and by A. Fröhlich and J. C. Shepherdson in which the effect of the existence of computable presentations which are non-equivalent from the viewpoint of their algorithmic properties was first discovered. Today there are many papers by various authors devoted to investigations of such questions. The present paper deals with the question of inheritance of the properties of autostability and non-autostability relative to strong constructivizations under elementary extensions for almost prime models.
Bibliography: 37 titles.

Keywords: computable model, constructive model, strongly constructive model, autostability, prime model, almost prime model, Ehrenfeucht theory, decidable theory, decidable model.

DOI: https://doi.org/10.4213/rm9373

Full text: PDF file (745 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:5, 901–935

Bibliographic databases:

Document Type: Article
UDC: 517.1+519.5
MSC: Primary 03C57; Secondary 03C35, 03D45, 03D80
Received: 29.06.2010

Citation: S. S. Goncharov, “On autostability of almost prime models relative to strong constructivizations”, Uspekhi Mat. Nauk, 65:5(395) (2010), 107–142; Russian Math. Surveys, 65:5 (2010), 901–935

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Goncharov, “Degrees of autostability relative to strong constructivizations”, Proc. Steklov Inst. Math., 274 (2011), 105–115  mathnet  crossref  mathscinet  isi
    2. E. B. Fokina, S. S. Goncharov, V. Harizanov, O. V. Kudinov, D. Turetsky, “Index sets for $n$-decidable structures categorical relative to $m$-decidable presentations”, Algebra and Logic, 54:4 (2015), 336–341  mathnet  crossref  crossref  mathscinet  isi
  • ”спехи математических наук Russian Mathematical Surveys
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