Self-fullness for ceers
Uri Andrews, Noah Schweber, Andrea Sorbi · arXiv (Cornell University) · 2019
We examine the property of self-fullness of computably enumerable equivalence relations (ceers) and its relation to the uniform join operation. We answer a question raised by Andrews and Sorbi by showing that there are self-full ceers $X$ and $Y$ so that $X\oplus Y$ is non-self-full. We then define and examine the collection of hereditarily self-full ceers, which are the self-full ceers $X$ so that for any self-full $Y$, $X\oplus Y$ is also self-full. We show that every dark ceer is hereditarily self-full, and that there are light ceers which are hereditarily self-full.