On generic structures with a strong amalgamation property

Journal of Symbolic Logic 74 (3):721-733 (2009)

Abstract
Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We show that the theory of the generic model of $K_\alpha $ is AE-axiomatizable for any α
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DOI 10.2178/jsl/1245158082
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References found in this work BETA

Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Analytic Zariski Structures and the Hrushovski Construction.Nick Peatfield & Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (2):127-180.
A Note on Generic Projective Planes.Koichiro Ikeda - 2002 - Notre Dame Journal of Formal Logic 43 (4):249-254.

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Citations of this work BETA

On Rational Limits of Shelah–Spencer Graphs.Justin Brody & M. C. Laskowski - 2012 - Journal of Symbolic Logic 77 (2):580-592.
On Superstable Generic Structures.Koichiro Ikeda & Hirotaka Kikyo - 2012 - Archive for Mathematical Logic 51 (5-6):591-600.

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