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$\Sigma$-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.
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English version:
Siberian Mathematical Journal, 2010, 51:3, 515–524
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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
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\jour Siberian Math. J.
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\issue 3
\pages 515--524
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http://mi.mathnet.ru/eng/smj2115 http://mi.mathnet.ru/eng/smj/v51/i3/p649
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