## Constructing $\omega $-stable structures: Computing rank

### Volume 170 / 2001

Fundamenta Mathematicae 170 (2001), 1-20
MSC: Primary 03C60.
DOI: 10.4064/fm170-1-1

#### Abstract

This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and $U$-rank of the infinite rank $\omega $-stable theories constructed by variants of Hrushovski's methods. Sample result: For every $k< \omega $, there is an $\omega $-stable expansion of any algebraically closed field which has Morley rank $\omega \times k$. We include a corrected proof of the lemma in [1] establishing that the generic model is $\omega $-saturated in the rank 2 case.