Archive for Mathematical Logic

, Volume 57, Issue 7–8, pp 769–794 | Cite as

Model completeness of generic graphs in rational cases

  • Hirotaka KikyoEmail author


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.


Hrushovski’s amalgamation construction Model completeness 

Mathematics Subject Classification

03C10 03C13 03C25 03C30 


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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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Graduate School of System InformaticsKobe UniversityKobeJapan

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