Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudofinite structures and simplicity   We explore a notion of pseudofinite dimension, introduced by Hrushovski and
Wagner, on an infinite ultraproduct of finite structures. Certain conditions on
pseudofinite dimension are identified that guarantee simplicity or
supersimplicity of the underlying theory, and that a drop in pseudofinite
dimension is equivalent to forking. Under a suitable assumption, a
measure-theoretic condition is shown to be equivalent to local stability. Many
examples are explored, including vector spaces over finite fields viewed as
2-sorted finite structures, and homocyclic groups. Connections are made to
products of sets in finite groups, in particular to word maps, and a
generalization of Tao's algebraic regularity lemma is noted.

32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph