Related papers: Chain conditions in dependent groups

We prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end.

Within the conventional framework of standard linear response theory we have derived exact results for the initial static susceptibilities of nonuniform spin-1/2 Ising chains. The results obtained permit one to study regularly…

In this Note we study the groups $G$ satisfying condition $(\mathcal{N},n)$, that is, every subset of $G$ with $n+1$ elements contains a pair $\{x,y\}$ such that the subgroup $<x,y>$ is nilpotent.

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also…

We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so…

Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…

E. Hrushovski proved that the theory of difference-differential fields of characteristic zero has a model-companion. We denote it DCFA. In this paper we study definable groups in a model of DCFA. First we prove that such a group is embeds…

It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here we prove based upon an analysis…

In this paper we consider the inductive Alperin--McKay condition for isolated blocks of groups of Lie type $B$ and $C$. This finishes the verification of the inductive condition for groups of this type.

We introduce $\infty$-type theories as an $\infty$-categorical generalization of the categorical definition of type theories introduced by the second named author. We establish analogous results to the previous work including the…

We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…

Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…

The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…

We prove a rigidity theorem for morphisms from products of open subschemes of the projective line into solvable groups not containing a copy of $\Ga$ (for example, wound unipotent groups). As a consequence, we deduce several structural…

We establish a one-to-one correspondence between one-sided and two-sided regular systems of conditional probabilities on the half-line that preserves the associated chains and Gibbs measures. As an application, we determine uniqueness and…

We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mixed Shimura varieties. It allows us to define all basic…

We prove an upper bound for the number of cyclic transitive subgroups in a finite permutation group and clarify the structure of the groups for which this bound becomes sharp. We also give an application in the theory of number fields.