5 papers
Switching Categoricity Behavior with a Given Degree
David Gonzalez, Java Darleen Villano, José Jeremías Valenzuela Morales
Given a noncomputable, computably enumerable set , we construct a computable structure such that any two computable copies of are computably isomorphic while there are t…
Extensions of categoricity relative to a degree
Java Darleen Villano
In this paper, we apply the machinery developed in arXiv:2401.06641(2) to study the behavior of computable categoricity relativized to non-c.e. degrees. In particular, we show that…
The Ginsburg--Sands theorem and computability theory
Heidi Benham, Andrew De Lapo, Damir Dzhafarov +2
The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on :…
Computable categoricity relative to a c.e. degree
Java Darleen Villano
A computable graph is computably categorical relative to a degree if and only if for all -computable copies of , t…
Normality, Relativization, and Randomness
Wesley Calvert, Emma Grunner, Elvira Mayordomo +2
Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized…