Related papers: A model theoretic study of right-angled buildings
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a…
In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite…
We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through…
We study convex subsets of buildings, discuss some structural features and derive several characterizations of buildings.
We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…
We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural…
We show that every Coxeter group that is not virtually abelian and for which all labels in the corresponding Coxeter graph are powers of 2 or infinity can be mapped onto uncountably many infinite 2-groups which, in addition, may be chosen…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free,…
Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any given number field is finite by combining Amerik's theorem…
We investigate the question of when free structures of infinite rank (in a variety) possess model-theoretic properties like categoricity in higher power, saturation, or universality. Concentrating on left $R$-modules we show, among other…
In this paper, we investigate a relation between finite graphs, simplicial flag complexes and right-angled Coxeter groups, and we provide a class of reconstructible finite graphs. We show that if $\Gamma$ is a finite graph which is the…
The main theme of this paper is higher virtual algebraic fibering properties of right-angled Coxeter groups (RACGs), with a special focus on those whose defining flag complex is a finite building. We prove for particular classes of finite…
We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte's tree decomposition of 2-connected graphs into 3-connected blocks.…
This expository paper treats the model theory of probability spaces using the framework of continuous $[0,1]$-valued first order logic. The metric structures discussed, which we call probability algebras, are obtained from probability…
Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality…
To any finite graph $X$ (viewed as a topological space) we assosiate some explicit compact metric space ${\cal X}^r(X)$ which we call {\it the reflection tree of graphs $X$}. This space is of topological dimension $\le1$ and its connected…
A ring $\Lambda$ is called right K\"othe if every right $\Lambda$-module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right K\"othe rings in terms of their Coxeter valued quivers. Also we…
We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…