Related papers: Big Ramsey Degrees and Infinite Languages
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
We study the tractability of conjunctive query answering for queries with unbounded arity. It is well known that tractability of the problem can be characterised in terms of the queries treewidth under the assumption of bounded arity. We…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
Hindman's theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. Ramsey algebras are structures that satisfy an analogue of Hindman's Theorem. This paper introduces Ramsey algebras and…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic structures.…
Despite the growing promise of large language models (LLMs) in automated essay scoring (AES), empirical findings regarding their reliability compared to human raters remain mixed. Following the PRISMA 2020 guidelines, we synthesized 65…
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March…
Large Language Models (LLMs) have become capable of generating highly fluent text in certain languages, without modules specially designed to capture grammar or semantic coherence. What does this mean for the future of linguistic expertise…
In this paper we provide purely categorical proofs of two important results of structural Ramsey theory: the result of M.\ Soki\'c that the free product of Ramsey classes is a Ramsey class and the result of M.\ Bodirsky, M.\Pinsker and T.\…
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…
The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field should have finite finitistic dimension. Recently, this conjecture is reduced to studying finitistic dimensions for extensions of algebras. In this…
In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known…
Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions of $\mathbb{F}_p(t)$. As an application, we show that for…
Building on previous work of the author, for each finite triangle-free graph $\mathbf{G}$, we determine the equivalence relation on the copies of $\mathbf{G}$ inside the universal homogeneous triangle-free graph, $\mathcal{H}_3$, with the…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential…
We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and…