In pseudofinite structures, the non-standard size of definable sets often reveals important algebraic or model theoretic properties of the corresponding theories. In this talk, we will give two new examples of this correlation. One is between the coarse dimension and the transformal transcendental degree in certain class of pseudofinite difference fields. The other example is that in pseudofinite H-strucures which are built from one-dimensional asymptotic classes, the coarse dimension of a tuple corresponds to the coefficient of the leading term of SU-rank of this tuple. This is the first step to show that they are examples of multidimensional asymptotic classes (mac).
- Théorie des Modèles et Groupes