Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong ergodicity around countable products of countable equivalence
  relations   This paper deals with countable products of countable Borel equivalence
relations and equivalence relations "just above" those in the Borel
reducibility hierarchy. We show that if $E$ is strongly ergodic with respect to
$\mu$ then $E^\mathbb{N}$ is strongly ergodic with respect to $\mu^\mathbb{N}$.
We answer questions of Clemens and Coskey regarding their recently defined
$\Gamma$-jump operations, in particular showing that the $\mathbb{Z}^2$-jump of
$E_\infty$ is strictly above the $\mathbb{Z}$-jump of $E_\infty$. We study a
notion of equivalence relations which can be classified by infinite sequences
of "definably countable sets". In particular, we define an interesting example
of such equivalence relation which is strictly above $E_\infty^\mathbb{N}$,
strictly below $=^+$, and is incomparable with the $\Gamma$-jumps of countable
equivalence relations.
  We establish a characterization of strong ergodicity between Borel
equivalence relations in terms of symmetric models. The proofs then rely on a
fine analysis of the very weak choice principles "every sequence of $E$-classes
admits a choice sequence", for various countable Borel equivalence relations
$E$.

4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph