Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbit equivalence and sofic approximation   Given an ergodic probability measure preserving dynamical system $\G\acts
(X,\mu)$, where $\G$ is a finitely generated countable group, we show that the
asymptotic growth of the number of finite models for the dynamics, in the sense
of sofic approximations, is an invariant of orbit equivalence. We then prove an
additivity formula for free products with amenable (possibly trivial)
amalgamation. In particular, we obtain purely combinatorial proofs of several
results in orbit equivalence theory.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph