Related papers: Computably Enumerable Equivalence Relations
We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with…
We contribute to a recent research program which aims at revisiting the study of the complexity of word problems, a major area of research in combinatorial algebra, through the lens of the theory of computably enumerable equivalence…
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
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
We study reductions well suited to compare structures and classes of structures with respect to properties based on enumeration reducibility. We introduce the notion of a positive enumerable functor and study the relationship with…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations $R$ and $S$ on natural numbers, $R$ is computably…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…
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…
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…
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 look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
In computable topology, a represented space is called computably discrete if its equality predicate is semidecidable. While any such space is classically isomorphic to an initial segment of the natural numbers, the computable-isomorphism…
A computably enumerable equivalence relation (ceer) $X$ is called self-full if whenever $f$ is a reduction of $X$ to $X$ then the range of $f$ intersects all $X$-equivalence classes. It is known that the infinite self-full ceers properly…
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…