Related papers: All Difference Family Structures arise from Groups
We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…
We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is…
Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of…
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
We prove a result of cohomology and base change for families of coherent systems over a curve. We use that in order to prove the existence of (non-split, non-degenerate) universal families of extensions for families of coherent systems (in…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and…
Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…
The main result of this paper is that every naturally reductive space can be explicitly constructed from the construction in \cite{Storm2018}. This gives us a general formula for any naturally reductive space and from this we prove…
The seceder model illustrates how the desire to be different than the average can lead to formation of groups in a population. We turn the original, agent based, seceder model into a model of network evolution. We find that the structural…
For families of all theories of arbitrary given languages we describe ranks and degrees. In particular, we characterize (non-)totally transcendental families. We apply these characterizations for the families of all theories of given…
We construct a new family of groups that is non-contracting and weakly regular branch over the derived subgroup. This gives the first example of an infinite family of groups acting on a $d$-adic tree, with $d \geq 2$, with these properties.
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…