Related papers: Generically Computable Equivalence Structures and …
For a class $\mathcal K$ of countable relational structures, a countable Borel equivalence relation $E$ is said to be $\mathcal K$-structurable if there is a Borel way to put a structure in $\mathcal K$ on each $E$-equivalence class. We…
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature,…
We examine the degree structure $\mathbf{ER}$ of equivalence relations on $\omega$ under computable reducibility. We examine when pairs of degrees have a join. In particular, we show that sufficiently incomparable pairs of degrees do not…
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a…
A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a…
We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theory, and the other one is a computational notion which is a…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…
Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…
We investigate two constructive approaches to defining quasi-compact and quasi-separated schemes (qcqs-schemes), namely qcqs-schemes as locally ringed lattices and as functors from rings to sets. We work in Homotopy Type Theory and…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…