Related papers: On a question of Krajewski's

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…

We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet $\{A_1, \overline{A}_1, \ldots, A_m,…

J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has evolved into an extensive theory of canonical extensions of lattice-based algebras. After reviewing this evolution we make two contributions.…

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…

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 study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the…

We prove that for any integers $\alpha, \beta > 1$, the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1,<, +, \alpha^{\mathbb{N}}, \beta^{\mathbb{N}}\rangle$ is decidable (where $\alpha^{\mathbb{N}}$…

We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…

Let $A$ be a unital separable \CA and $B=C\otimes {\cal K},$ where $C$ is a unital \CA. Let $\tau: A\to M(B)/B$ be a weakly unital full essential extensions of $A$ by $B.$ We show that there is a bijection between a quotient group of…

Let $\kappa,\lambda$ be regular cardinals, $\lambda\le\kappa$, let $\varphi$ be a sentence of the language $\mathcal L_{\kappa,\lambda}$ in a given signature, and let $\vartheta(\varphi)$ express the fact that $\varphi$ holds in a submodel,…

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…

We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is…

Descriptive set theory was originally developed on Polish spaces. It was later extended to $\omega$-continuous domains [Selivanov 2004] and recently to quasi-Polish spaces [de Brecht 2013]. All these spaces are countably-based. Extending…

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…

Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…

``Completeness'' (i.e. probability conservation) is not usually satisfied in the cumulant expansion of the Anderson lattice when a reduced state space is employed for $U\to \infty $. To understand this result, the well known ``Chain''…

We consider the natural generalization of the notion of the order of a phantom map from the topological setting to triangulated categories. When applied to the derived category of the category of countable flat modules over a countable…

We prove conservativity results for weak K\H{o}nig's lemma that extend the celebrated result of Harrington (for $\Pi^1_1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form…

We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining…