Rank and dimension in difference-differential fields
The model companion DCFA of the theory of difference-differential fields of characteristic 0 is considered. It is known that the completions of DCFA are supersimple. The author computes their SU-rank and compares it and a notion of dimension based on the transcendence degree of realizations of types. In particular, an example of a definable set with SU-rank 1 but infinite dimension is provided. On the other hand it is shown that a definable subgroup of the additive group is finite-dimensional if and only if it has finite SU-rank.
scientific article; zbMATH DE number 5991007