Related papers: Relations enumerable from positive information
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…
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,…
Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
Given a countable mathematical structure, its Scott sentence is a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ that characterizes it among all countable structures. We can measure the complexity of a structure by the…
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
In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more…
We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…
We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group $\Gamma$ we introduce the $\Gamma$-jump. We study the elementary properties of the $\Gamma$-jumps and compare them with other…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rank-connectivity. In terms…
The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…
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…
Given a definably amenable approximate subgroup $A$ of a (local) group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ such that every definable superset of $H$ has positive…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed Cuntz class is path connected. This result applies in particular…
Proposition algebra is based on Hoare's conditional connective, which is a ternary connective comparable to if-then-else and used in the setting of propositional logic. Conditional statements are provided with a simple semantics that is…