Related papers: Myhill-Nerode Relation for Sequentiable Structures

We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…

Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode…

Formal (mixed) Hodge structures FHS are introduced in such a way that the Hodge realization of Deligne's 1-motives extends to a realization from Laumon's 1-motives to formal Hodge structures of level 1, providing an equivalence of…

Svenonius theorem reduces the problem of first-order definability to the problem of relationship between groups of permutations. In the present paper we use this approach to describe the lattice of definable relations for the structure of…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…

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…

Transducers extend finite state automata with outputs, and describe transformations from strings to strings. Sequential transducers, which have a deterministic behaviour regarding their input, are of particular interest. However, unlike…

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian…

We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…

For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by…

A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we examine minimal…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

Let $FI$ be a skeleton of the category of finite sets and injective maps, and $FI^m$ the product of $m$ copies of $FI$. We prove that if an $FI^m$-module is generated in degree $\leqslant d$ and related in degree $\leqslant r$, then its…

We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardinalities of definable sets: The condition asserts that…

We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categories as algebraic structures in $\mathbf{Prof}$, the monoidal…

A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…

We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…

The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…