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Model completeness of generic graphs in rational cases

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Abstract

Let \(\mathbf {K}_f\) be an ab initio amalgamation class with an unbounded increasing concave function f. We show that if the predimension function has a rational coefficient and f satisfies a certain assumption then the generic structure of \(\mathbf {K}_f\) has a model complete theory.

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Acknowledgements

The author appreciates valuable discussions with Koichiro Ikeda, Akito Tsuboi, Masanori Sawa, and Genki Tatsumi. The author also would like to appreciate the referee for the valuable comments. The author is supported by JSPS KAKENHI Grant Nos. 25400203 and 17K05345.

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Authors and Affiliations

  1. Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan

    Hirotaka Kikyo

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  1. Hirotaka Kikyo
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Correspondence to Hirotaka Kikyo.

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Kikyo, H. Model completeness of generic graphs in rational cases. Arch. Math. Logic 57, 769–794 (2018). https://doi.org/10.1007/s00153-017-0601-4

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  • DOI: https://doi.org/10.1007/s00153-017-0601-4

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