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Sib. Èlektron. Mat. Izv., 2008, Volume 5, Pages 200–210 (Mi semr100)  

This article is cited in 5 scientific papers (total in 5 papers)

Research papers

Index sets of prime model

E. N. Pavlovskii

Novosibirsk State University, Mechanics and Mathematics Department

Abstract: We prove that for every nontrivial language $\sigma$, the index set of the class of $d$-decidable prime computable models of $\sigma$ is $\Sigma_3^{0,d}\setminus\Sigma_3^{0,d}$-complete and that the index set of all prime computable models of $\sigma$ is $\Pi_{\omega+2}^0$-complete.

Keywords: prime model, computable model, index sets, model-theoretic constructions, hyperarithmetic hierarchy.

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Bibliographic databases:
UDC: 517.1, 519.5
MSC: 03C50, 03C52, 03C57, 03D35
Received February 14, 2008, published May 5, 2008

Citation: E. N. Pavlovskii, “Index sets of prime model”, Sib. Èlektron. Mat. Izv., 5 (2008), 200–210

Citation in format AMSBIB
\Bibitem{Pav08}
\by E.~N.~Pavlovskii
\paper Index sets of prime model
\jour Sib. \`Elektron. Mat. Izv.
\yr 2008
\vol 5
\pages 200--210
\mathnet{http://mi.mathnet.ru/semr100}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586631}


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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, “Index Sets of Almost Prime Constructive Models”, J. Math. Sci., 205:3 (2015), 355–367  mathnet  crossref
    2. S. S. Goncharov, M. I. Marchuk, “Index Sets of Autostable Relative to Strong Constructivizations Constructive Models”, J. Math. Sci., 205:3 (2015), 368–388  mathnet  crossref
    3. S. S. Goncharov, M. I. Marchuk, “Index sets of constructive models of bounded signature that are autostable relative to strong constructivizations”, Algebra and Logic, 54:2 (2015), 108–126  mathnet  crossref  crossref  mathscinet  isi
    4. S. S. Goncharov, M. I. Marchuk, “Index sets of constructive models of finite and graph signatures that are autostable relative to strong constructivizations”, Algebra and Logic, 54:6 (2016), 428–439  mathnet  crossref  crossref  mathscinet  isi
    5. M. I. Marchuk, “Razreshimaya kategorichnost pochti prostykh modelei signatury grafov”, Matem. tr., 24:1 (2021), 117–141  mathnet  crossref
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