Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly minimal groups with a new predicate   Fix a weakly minimal (i.e., superstable $U$-rank $1$) structure
$\mathcal{M}$. Let $\mathcal{M}^*$ be an expansion by constants for an
elementary substructure, and let $A$ be an arbitrary subset of the universe
$M$. We show that all formulas in the expansion $(\mathcal{M}^*,A)$ are
equivalent to bounded formulas, and so $(\mathcal{M},A)$ is stable (or NIP) if
and only if the $\mathcal{M}$-induced structure $A_{\mathcal{M}}$ on $A$ is
stable (or NIP). We then restrict to the case that $\mathcal{M}$ is a pure
abelian group with a weakly minimal theory, and $A_{\mathcal{M}}$ is mutually
algebraic (equivalently, weakly minimal with trivial forking). This setting
encompasses most of the recent research on stable expansions of
$(\mathbb{Z},+)$. Using various characterizations of mutual algebraicity, we
give new examples of stable structures of the form $(\mathcal{M},A)$. Most
notably, we show that if $(G,+)$ is a weakly minimal additive subgroup of the
algebraic numbers, $A\subseteq G$ is enumerated by a homogeneous linear
recurrence relation with algebraic coefficients, and no repeated root of the
characteristic polynomial of $A$ is a root of unity, then $(G,+,B)$ is
superstable for any $B\subseteq A$.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat