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On generic structures with a strong amalgamation property

Published online by Cambridge University Press:  12 March 2014

Koichiro Ikeda ,
Hirotaka Kikyo  and
Akito Tsuboi
Koichiro Ikeda
Affiliation:
Faculty of Business Administration, Hosei University, 2-17-1 Fujimi, Chiyoda, Tokyo 102-8160, Japan, E-mail: ikeda@hosei.ac.jp
Hirotaka Kikyo
Affiliation:
Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan, E-mail: kikyo@kobe-u.ac.jp
Akito Tsuboi
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan, E-mail: tsuboi@math.tsukuba.ac.jp
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Abstract

Let be a finite relational language and α = (αR: R ∈ ) a tuple with 0 < αR ≤ 1 for each R ∈ . Consider a dimension function

where each eR(A) is the number of realizations of R in A. Let Kα be the class of finite structures A such that δα (X) ≥ 0 for any substructure X of A. We show that the theory of the generic model of Kα is AE-axiomatizable for any α.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 721 - 733
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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