Related papers: Isomorphism and classification for countable struc…

The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions

We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…

In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…

A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is non-expansive. We also give a topological…

Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…

Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of…

We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…

We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…

The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…

We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…

For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

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…

By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…