3 papers
math.LO2025
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…
math.LO2025
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…
math.LO2025
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…