Related papers: Approximate Categoricity in Continuous Logic
We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…
In his article "Arithmetic Fujita Approximations", Huayi Chen introduces the notion of an approximable graded algebra and asks if any such algebra is a subalgebra of the graded section ring of a big line bundle on an algebraic variety. We…
We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as…
In this paper we prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-filtered colimits is a…
We show that every definable subset of an uncountably categorical pseudofinite structure has pseudofinite cardinality which is polynomial (over the rationals) in the size of any strongly minimal subset, with the degree of the polynomial…
We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…
We prove that, under some conditions, a linear nonautonomous difference system is Bylov's almost reducible to a diagonal one whose terms are contained in the Sacker and Sell spectrum of the original system. We also provide an example of the…
We study connections between definability in generalized descriptive set theory and large cardinals, under ZFC. We show that if $\kappa$ is a limit of measurables then there is no wellorder of a subset of $P(\kappa)$ of length…
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…
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek.
Recently Paw\l{}ucki showed that compact sets that are definable in some o-minimal structure admit triangulations of class $\mathcal{C}^p$ for each integer $p\geq 1$. In this work, we make use of these new techniques of triangulation to…
The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category $\mathsf{Top}$ of topological spaces and continuous functions, to study $\textit{compactly generated…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery,…
Through careful analysis of types inspired by [AGTW21] we characterize a notion of definable compactness for definable topologies in general o-minimal structures, generalizing results from [PP07] about closed and bounded definable sets in…
The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its…
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and…
A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. Its morphisms have been used in describing reductions between search problems in complexity theory. We describe…
These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…