On generic structures with a strong amalgamation property
Koichiro Ikeda, Hirotaka Kikyo, Akito Tsuboi · Journal of Symbolic Logic · 2009
Abstract Let be a finite relational language andα= (αR:R∈ ) a tuple with 0 <αR≤ 1 for eachR∈ . Consider a dimension function where eacheR(A)is the number of realizations ofRinA. LetKαbe the class of finite structuresAsuch thatδα(X)≥ 0 for any substructureXofA. We show that the theory of the generic model ofKαis AE-axiomatizable for anyα.