Related papers: On equationally Noetherian predicate structures
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and…
We study equations over relational structures that approximate groups and semigroups. For such structures we proved the criteria, when a direct power of such algebraic structures is equationally Noetherian.
We study systems of equations over graphs, posets and matroids. We give the criteria, when a direct power of such algebraic structures is equationally Noetherian. Moreover we prove that any direct power of a finite algebraic structure is…
In this article, we describe the relation between the properties of being equational noetherian and ascending chain condition on ideals of an arbitrary algebra. We also give a formulation of Hilbert's basis theorem for varieties of algebras…
We prove a noetherian criterion for a sequence of modules with linear maps between them. This generalizes a noetherian criterion of Gan and Li for infinite EI categories. We apply our criterion to the linear categories associated to certain…
The goal of this note is to present Kaplansky's proof of the Regular Element Property and to explain how this argument can be adapted to the case of a coherent, strongly discrete and Noetherian (with an inductive definition of Noetherian)…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
We give an elementary proof prove of the preservation of the Noetherian condition for commutative rings with unity $R$ having at least one finitely generated ideal $I$ such that the quotient ring is again finitely generated, and $R$ is…
A necessary and sufficient compactness criterion in Schauder Spaces is proved.
The aim of this paper is to compare and contrast the class of residually finite groups with the class of equationally Noetherian groups - groups over which every system of coefficient-free equations is equivalent to a finite subsystem. It…
In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programming language. We want to say that a set is…
We show how security type systems from the literature of language-based noninterference can be represented more directly as predicates defined by structural recursion on the programs. In this context, we show how our uniform syntactic…
In this paper we consider noetherianity for formulas of propositional and predicate calculus over different fields. Three types of noetherianity are considered: standard noetherianity, logical noetherianity and denumerable noetherianity.
A first-order theory is Noetherian with respect to the collection of formulae $\mathcal{F}$ if every definable set is a Boolean combination of instances of formulae in $\mathcal{F}$ and the topology whose subbasis of closed sets is the…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
We study equations over boolean algebras with distinguished elements. We prove the criteria, when a boolean algebra is equationally Noetherian, weakly equationally Noetherian, $\mathbf{q}_\omega$-compact or $\mathbf{u}_\omega$-compact. Also…
We prove that any finite-degree polynomial functor is topologically Noetherian. This theorem is motivated by the recent resolution of Stillman's conjecture and a recent Noetherianity proof for the space of cubics. Via work by…
We give an algebraic proof of the criterion for hereditary structural completeness of an intermediate logic, or, equivalently, of the primitiveness of a variety of Heyting algebras.
The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of…
Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group $(G, f)=\mathrm{der}_{\theta, b}(G, \cdot)$ is equational noetherian, if and only if the ordinary group $(G, \cdot)$ is equational…