Strict Superstablity and Decidability of Certain Generic Graphs

We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $\alpha \in \omega +1\mathrm{\backslash }\{0\}$ we introduce a strictly superstable theory of U-rank $\alpha \mathrm{.}$ Furthermore, we show that these theories are decidable and pseudofinite.