Siberian Mathematical Journal

, Volume 49, Issue 3, pp 512–523 | Cite as

Estimation of the algorithmic complexity of classes of computable models

  • E. N. Pavlovskii


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


computable model index set 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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