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Elementary submodels of parametrizable models

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Abstract

We introduce the notion of F-parametrizable model and prove some general results on elementary submodels of F-parametrizable models. Using this notion, we can uniformly characterize all elementary submodels for the field of real numbers and for the group of all permutations on natural numbers in the first order language as well as in the language of hereditarily finite superstructures. Assuming the constructibility axiom, we obtain a simpler characterization of elementary submodels of F-parametrizable models and prove some additional properties of the structure of their elementary submodels.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. S. Morozov

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  1. A. S. Morozov
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Original Russian Text Copyright © 2006 Morozov A. S.

The author was supported by RFBR-DFG (Grant 01-01-04003 NNIOa), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.2003.1), and the Russian Science Support Foundation.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 595–612, May–June, 2006.

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Morozov, A.S. Elementary submodels of parametrizable models. Sib Math J 47, 491–504 (2006). https://doi.org/10.1007/s11202-006-0061-2

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  • DOI: https://doi.org/10.1007/s11202-006-0061-2

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