Definability and continuity of the SU-rank in unidimensional supersimple theories

TL;DR

This paper proves that in unidimensional supersimple theories, the SU-rank is continuous and the D-rank is definable, advancing understanding of rank properties in model theory.

Contribution

It establishes the continuity of SU-rank and definability of D-rank specifically in unidimensional supersimple theories, providing new insights into their structure.

Findings

SU-rank is continuous in unidimensional supersimple theories

D-rank is definable in these theories

Advances understanding of rank behavior in model theory

Abstract

We prove, in particular, that in a supersimple unidimensional theory the $SU$-rank is continuous and the $D$-rank is definable.