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Estimation of the algorithmic complexity of classes of computable models

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Abstract

We estimate the algorithmic complexity of the index set of some natural classes of computable models: finite computable models (Σ 02 -complete), computable models with ω-categorical theories (Δ 0ω -complex Π 0 ω+2 -set), prime models (Δ 0ω -complex Π 0 ω+2 -set), models with ω 1-categorical theories (Δ 0ω -complex Σ 0 ω+1 -set. We obtain a universal lower bound for the model-theoretic properties preserved by Marker’s extensions (Δ 0ω .

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    E. N. Pavlovskii

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  1. E. N. Pavlovskii
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Correspondence to E. N. Pavlovskii.

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Original Russian Text Copyright © 2008 Pavlovskiĭ E. N.

The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-4413.2006.1) and the Program “Universities of Russia” (Grant UR.04.01.198).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 3, pp. 635–650, May–June, 2008.

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Pavlovskii, E.N. Estimation of the algorithmic complexity of classes of computable models. Sib Math J 49, 512–523 (2008). https://doi.org/10.1007/s11202-008-0049-1

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  • DOI: https://doi.org/10.1007/s11202-008-0049-1

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