|
This article is cited in 2 scientific papers (total in 2 papers)
$\Sigma$-definability of uncountable models of $c$-simple theories
A. I. Stukachevab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
Abstract:
We show that each $c$-simple theory with an additional discreteness condition has an uncountable model $\Sigma$-definable in $\mathbb{HF}(\mathbb L)$, where $\mathbb L$ is a dense linear order. From this we establish the same for all $c$-simple theories of finite signature that are submodel complete.
Keywords:
computable theory, model theory, constructive model, admissible set.
 Full text:
PDF file (357 kB)
References:
PDF file
HTML file
English version:
Siberian Mathematical Journal, 2010, 51:3, 515–524
Bibliographic databases:
   
UDC:
510.5
Received: 08.12.2008
Citation:
A. I. Stukachev, “$\Sigma$-definability of uncountable models of $c$-simple theories”, Sibirsk. Mat. Zh., 51:3 (2010), 649–661; Siberian Math. J., 51:3 (2010), 515–524
Citation in format AMSBIB
\Bibitem{Stu10}
\by A.~I.~Stukachev
\paper $\Sigma$-definability of uncountable models of $c$-simple theories
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 3
\pages 649--661
\mathnet{http://mi.mathnet.ru/smj2115}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2722678}
\zmath{https://zbmath.org/?q=an:1209.03030}
\transl
\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 3
\pages 515--524
\crossref{https://doi.org/10.1007/s11202-010-0054-z}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279087500016}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953976351}
Linking options:
http://mi.mathnet.ru/eng/smj2115 http://mi.mathnet.ru/eng/smj/v51/i3/p649
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
A. S. Morozov, “$\Sigma$-preorderings in ${\mathbb{HF}(\mathbb{R})}$”, Algebra and Logic, 58:5 (2019), 405–416
 -
A. I. Stukachev, “Intervalnye rasshireniya poryadkov i temporalnye approksimatsionnye prostranstva”, Sib. matem. zhurn., 62:4 (2021), 894–910
|
| Number of views: |
| This page: | 254 | | Full text: | 74 | | References: | 31 | | First page: | 2 |
|
Terms of Use