Related papers: Pseudofiniteness in Hrushovski Constructions
Having been unclear how to define that a domain is strictly pseudoconvex in the infinite-dimensional setting, we develop a general theory having Banach spaces in mind. We first focus on finite dimension and eliminate the need of two degrees…
Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…
Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ of type $A_{n}$. Our construction is compatible…
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
The profile of a relational structure $R$ is the function $\varphi_R$ which counts for every integer $n$ the number $\varphi_R(n)$, possibly infinite, of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures…
We show that if $\mathsf V$ is a semigroup pseudovariety containing the finite semilattices and contained in $\mathsf {DS}$, then it has a basis of pseudoidentities between finite products of regular pseudowords if, and only if, the…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{infty, omega} formula with counting quantifiers defines a linear…
We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field,…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
In this paper, proof of the {\it Kurlberg-Rudnick supremum conjecture} for the quantum Hannay-Berry model is presented. This conjecture was stated in P. Kurlberg's lectures at Bologna 2001 and Tel-Aviv 2003. The proof is a primer…
We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or…
A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $sib(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism.…
We explore new interactions between finite model theory and classical streams of universal algebra and semigroup theory. A key result is an example of finite algebras whose variety is not finitely axiomatisable in first order logic, but…
We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…