Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Definability of groups in $\aleph_0$-stable metric structures   We prove that in a continuous $\aleph_0$-stable theory every type-definable
group is definable. The two main ingredients in the proof are:
\begin{enumerate} \item Results concerning Morley ranks (i.e., Cantor-Bendixson
ranks) from \cite{BenYaacov:TopometricSpacesAndPerturbations}, allowing us to
prove the theorem in case the metric is invariant under the group action; and
\item Results concerning the existence of translation-invariant definable
metrics on type-definable groups and the extension of partial definable metrics
to total ones. \end{enumerate}

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat