4 papers
Dimension and measure in pseudofinite H-structures
Alexander Berentein, Dario Garcia, Tingxiang Zou
We study H-structures associated to SU-rank 1 measurable structures. We prove that the SU-rank of the expansion is continuous and that it is uniformly definable in terms of the par…
Unimodularity unified
Darío García, Frank Olaf Wagner
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and…
Ordered asymptotic classes of finite structures
Darío García
In this paper we introduce the concept of O-asymptotic classes of finite structures, melding ideas coming from 1-dimensional asymptotic classes and o-minimality. The results we pre…
Pseudofinite structures and simplicity
Dario Garcia, Dugald Macpherson, Charles Steinhorn
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension a…