Related papers: On Rayner structures
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…
Generalised indiscernibles highlight a strong link between model theory and structural Ramsey theory. In this paper, we use generalised indiscernibles as tools to prove results in both these areas. More precisely, we first show that a…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
Krieger's embedding theorem provides necessary and sufficient conditions for an arbitrary subshift to embed in a given topologically mixing $\mathbb{Z}$-subshift of finite type. For some $\mathbb{Z}^d$-subshifts of finite type, Lightwood…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…
It is well known that all torsors under an affine algebraic group over an algebraically closed field are trivial. We note that under suitable conditions this also holds if the the group is not necessarily of finite type. This has an…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We study combinatorial properties of the subshift induced by the substitution that describes Lysenok's presentation of Grigorchuk's group of intermediate growth by generators and relators. This subshift has recently appeared in two…
Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…
In algebraic geometry specialisations and valuations play and important role. In this paper we start investigating analogous structures for Zariski structures. Specifically, we look into the existence and uniqueness properties of extensions…
We associate ergodic properties to some subsets of the natural numbers. For any given family of subsets of the natural numbers one may study the question of occurrence of certain "algebraic patterns" in every subset in the family. By…
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
We discuss certain special cases of algebraic approximants that are given as zeroes of so-called "effective characteristic polynomials" and their generalization to a multiseries setting. These approximants are useful for the convergence…
We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding…
A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well chosen directions. We describe a set of…
A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian…
This inquiry is based on both the construction of generalized incidence rings due to Gene Abrams and the construction of good group gradings of incidence algebras due to Molli Jones. We provide conditions for a generalized incidence ring to…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…