Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coxeter Groups and Abstract Elementary Classes: The Right-Angled Case   We study classes of right-angled Coxeter groups with respect to the strong
submodel relation of parabolic subgroup. We show that the class of all
right-angled Coxeter group is not smooth, and establish some general
combinatorial criteria for such classes to be abstract elementary classes, for
them to be finitary, and for them to be tame. We further prove two
combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter
group of arbitrary rank. The combination of these results translate into a
machinery to build concrete examples of $\mathrm{AECs}$ satisfying given
model-theoretic properties. We exhibit the power of our method constructing
three concrete examples of finitary classes. We show that the first and third
class are non-homogeneous, and that the last two are tame, uncountably
categorical and axiomatizable by a single $L_{\omega_{1}, \omega}$-sentence. We
also observe that the isomorphism relation of any countable complete
first-order theory is $\kappa$-Borel reducible (in the sense of generalized
descriptive set theory) to the isomorphism relation of the theory of
right-angled Coxeter groups whose Coxeter graph is an infinite random graph.

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs