Some remarks on Hrushovski constructions in irrational case (Model theoretic aspects of the notion of independence and dimension)

Abstract

In rational case, the index of a free amalgamation class mathscr{C}{f} is infinite if and only if the theory of the Fraïssé limit mathcal{M}_{f} of mathscr{C}{f} is model complete. On the other hand, it is unknown whether the same assertion holds or not in irrational case. However, we can construct a free amalgamation class with the model complete theory from a given class. In this paper, we will introduce the constructions of free amalgamation classes with generic structures having model complete theories.