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Σ-definability of uncountable models of c-simple theories

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Abstract

We show that each c-simple theory with an additional discreteness condition has an uncountable model Σ-definable in ℍ\( \mathbb{H} \)(\( \mathbb{L} \)), 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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. I. Stukachev

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  1. A. I. Stukachev
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Correspondence to A. I. Stukachev.

Additional information

Dedicated to Yurĭ Leonidovich Ershov.

Original Russian Text Copyright © 2010 Stukachev A. I.

The author was supported by the Russian Foundation for Basic Research (Grants 06-01-04002-NNIOa, 08-01-00442a, and 09-01-12140-ofi_m), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-335.2008.1), and the Lavrent’ev Young Scientists Competition of the Russian Academy of Sciences (Resolution No. 43 of 04.02.2010).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 649–661, May–June, 2010.

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Stukachev, A.I. Σ-definability of uncountable models of c-simple theories. Sib Math J 51, 515–524 (2010). https://doi.org/10.1007/s11202-010-0054-z

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  • DOI: https://doi.org/10.1007/s11202-010-0054-z

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