On generic structures with a strong amalgamation property
Koichiro Ikeda, Hirotaka Kikyo, and Akito Tsuboi
Source: J. Symbolic Logic
Volume 74, Issue 3
(2009), 721-733.
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
δα(A) = |A| - ΣR
∈ ℒα_R e_R(A)
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158082
Digital Object Identifier: doi:10.2178/jsl/1245158082
Zentralblatt MATH identifier:
05609387
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