Strict Superstablity and Decidability of Certain Generic Graphs

Abstract

We show that the Hrushovski–Fraïssé limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each α∈ ω+ 1 \ { 0 } we introduce a strictly superstable theory of U-rank α. Furthermore, we show that these theories are decidable and pseudofinite. © 2019, Iranian Mathematical Society.