Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\bigoplus_{p\in P}\mathbb{F}_p$-Systems as Abramov Systems   Let $\mathcal{P}$ be an (unbounded) countable multiset of primes, let
$G=\bigoplus_{p\in P}\mathbb{F}_p$. We study the $k$'th universal
characteristic factors of an ergodic probability system $(X,\mathcal{B},\mu)$
with respect to some measure preserving action of $G$. We find conditions under
which every extension of these factors is generated by phase polynomials and we
give an example of an ergodic $G$-system that is not Abramov. In particular we
generalize the main results of Bergelson Tao and Ziegler who proved a similar
theorem in the special case $P=\{p,p,p,...\}$ for some fixed prime $p$. In a
subsequent paper we use this result to prove a general structure theorem for
ergodic $\bigoplus_{p\in P}\mathbb{F}_p$-systems.

21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat