# Strict Superstablity and Decidability of Certain Generic Graphs

## TL;DR

This paper constructs a series of strictly superstable theories of various U-ranks from certain classes of trees, demonstrating their decidability and pseudofiniteness.

## Contribution

It introduces a family of strictly superstable theories with prescribed U-ranks derived from Hrushovski-raisse limits of tree classes, establishing their decidability and pseudofiniteness.

## Key findings

- For each , a strictly superstable theory of U-rank  is constructed.
- These theories are shown to be decidable.
- Theories are also proven to be pseudofinite.

## Abstract

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\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $ \alpha. $ Furthermore, we show that these theories are decidable and pseudofinite.