ON mathrm{K}_{f} IN IRRATIONAL CASES (Model theoretic aspects of the notion of independence and dimension)

Consider an ab initio amalgamation class mathrm{K}_{f} with an unbounded increasing concave function f. We conjecture that if mathrm{K}_{f} has the free amalgamation property then the generic structure for mathrm{K}_{f} has a model complete theory. We consider the case where the predimension function has an irrational coefficient. We show some statements which seem to be useful to show our conjecture