Java Darleen Villano
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View article: Extensions of categoricity relative to a degree
Extensions of categoricity relative to a degree Open
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 we can build a computable structure which is not computabl…
View article: The Ginsburg--Sands theorem and computability theory
The Ginsburg--Sands theorem and computability theory Open
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 $ω$: indiscrete, discrete, initial segment, final segment, and …
View article: Computable categoricity relative to a c.e. degree
Computable categoricity relative to a c.e. degree Open
A computable graph $\mathcal{G}$ is computably categorical relative to a degree $\mathbf{d}$ if and only if for all $\mathbf{d}$-computable copies $\mathcal{B}$ of $\mathcal{G}$, there is a $\mathbf{d}$-computable isomorphism $f:\mathcal{G…
View article: Normality, Relativization, and Randomness
Normality, Relativization, and Randomness Open
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 number representation systems. We explore the concepts of …