Related papers: Preservation theorems for Tarski's relation algebr…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
We give a complete classification of finitely generated virtually free groups up to $\forall\exists$-elementary equivalence. As a corollary, we give an algorithm that takes as input two finite presentations of virtually free groups, and…
The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient…
Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed…
A family of partial functions of a class of algebras $\mathsf{K}$ is said to be an implicit operation of $\mathsf{K}$ when it is defined by a first order formula and it is preserved by homomorphisms. In this work, we develop the theory of…
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…
In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, or algebraic information about the embedded group. We discuss…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as…
Euclid's reasoning is essentially constructive. Tarski's elegant and concise first-order theory of Euclidean geometry, on the other hand, is essentially non-constructive, even if we restrict attention (as we do here) to the theory with…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…
We construct an infinite finitely generated recursively presented residually finite algorithmically finite group $G$ answering thereby a question of Myasnikov and Osin. Moreover, $G$ is "very infinite" and "very algorithmically finite" in…
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…