Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T13:03:27.528Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get accessRights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Baldwin, J. T. and Shelah, S., Randomness and semigenericity, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 1359–1376.CrossRefGoogle Scholar
[2]Baldwin, J. T. and Shi, N., Stable generic structures, Annals of Pure and Applied Logic, vol. 79 (1996), pp. 1–35.CrossRefGoogle Scholar
[3]Hrushovski, E., A stable ℵ0-categorical pseudoplane, preprint, 1988.Google Scholar
[4]Ikeda, K., A note on generic projective planes, Notre Dame Journal of Formal Logic, vol. 43 (2002), no. 4, pp. 249–254.CrossRefGoogle Scholar
[5]Kikyo, H., On predimensions of finite structures, Kokyuroku of RIMS in Kyoto University, vol. 1450 (2005), pp. 75–82.Google Scholar
[6]Laskowski, M. C., A simpler axiomatization of the Shelah–Spencer almost sure theories, Israel Journal of Mathematics, vol. 161 (2007), pp. 157–186.CrossRefGoogle Scholar
[7]Peatfield, N. and Zilber, B., Analytic Zariski structures and the Hrushovski construction, Annals of Pure and Applied Logic, vol. 132 (2005), pp. 127–180.CrossRefGoogle Scholar
[8]Spencer, J., The strange logic of random graphs, Springer, 2001.CrossRefGoogle Scholar
[9]Wagner, F. O., Relational structures and dimensions, Automorphisms of first-order structures, Oxford Science Publications, Oxford University Press, New York, 1994, pp. 153–180.CrossRefGoogle Scholar