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This paper investigates the effective categoricity of ultrahomogeneous structures. It is shown that any computable ultrahomogeneous structure is $\Delta^0_2$ categorical. A structure A is said to be weakly ultrahomogeneous if there is a…

Logic · Mathematics 2016-08-04 Francis Adams , Douglas Cenzer

The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…

Computational Complexity · Computer Science 2020-12-09 L. Gordeev , E. H. Haeusler

We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…

Numerical Analysis · Mathematics 2026-05-25 Eloïse Barthelemy , Geneviève Dusson , Camille Hernandez , Liwei Zhang

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

Logic in Computer Science · Computer Science 2023-02-15 Nicolai Kraus , Jakob von Raumer

In previous work, joint with Bux, Fluch, Marschler and Witzel, we proved that the braided Thompson groups are of type $\textrm{F}_\infty$. The proof utilized certain contractible cube complexes, which in this paper we prove are CAT(0). We…

Group Theory · Mathematics 2021-04-13 Matthew C. B. Zaremsky

We remark on the claim that the string-net model of Levin and Wen is a microscopic Hamiltonian formulation of the Turaev-Viro topological quantum field theory. Using simple counterexamples we indicate where interesting extra structure may…

Strongly Correlated Electrons · Physics 2011-03-22 Spencer D. Stirling

We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…

Quantum Physics · Physics 2026-03-06 Naren Manjunath , Vieri Mattei , Apoorv Tiwari , Tyler D. Ellison

Let $\alpha=(A_g,\alpha_g)_{g\in G}$ be a group-type partial action of a connected groupoid $G$ on a ring $A=\bigoplus_{z\in G_0}A_z$ and $B=A\star_{\alpha}G$ the corresponding partial skew groupoid ring. In the first part of this paper we…

Rings and Algebras · Mathematics 2021-03-09 Dirceu Bagio , Víctor Marín , Héctor Pinedo

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

Logic · Mathematics 2026-01-21 Meng-Che "Turbo" Ho , Martin Ritter , Luca San Mauro

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

Programming Languages · Computer Science 2020-09-22 Kazuhiko Sakaguchi

CM-type projective varieties X of complex dimension n are characterized by their CM-type rational Hodge structures on the cohomology groups. One may impose such a condition in a weakest form when the canonical bundle of X is trivial; the…

Algebraic Geometry · Mathematics 2024-01-25 Masaki Okada , Taizan Watari

We describe a Martin-L\"of style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…

Programming Languages · Computer Science 2019-01-14 Brigitte Pientka , Andreas Abel , Francisco Ferreira , David Thibodeau , Rebecca Zucchini

We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…

Logic in Computer Science · Computer Science 2020-10-05 Keng Meng Ng , Nazanin R. Tavana , Yue Yang

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

Operator Algebras · Mathematics 2021-01-12 Clément Dell'Aiera , Rufus Willett

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

Dynamical Systems · Mathematics 2026-04-14 Chris Bruce , Xin Li

Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…

Category Theory · Mathematics 2008-02-26 Jonathan A. Cohen

We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion ($\mathsf{ATR}_0$) from the point of view of computability-theoretic reducibilities, in particular Weihrauch…

Logic · Mathematics 2019-05-17 Jun Le Goh

A cohesive power of a computable structure is an effective ultrapower where a cohesive set acts as an ultrafilter. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and the rationals.…

Logic · Mathematics 2023-10-11 Paul Shafer

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

Group Theory · Mathematics 2020-01-29 Jesús Ávila , Víctor Marín , Héctor Pinedo

Let $G$ be a reductive group over a nonarchimedean local field $F$. In the quest for a classification of irreducible smooth representations of $G$, it is critical to understand the case of supercuspidal representations -- those whose matrix…

Representation Theory · Mathematics 2023-11-21 Alexandre Afgoustidis