A symmetric $\beta$-model

Abstract

We prove that there exists a countable $\beta$-model in which, for all reals $X$ and $Y$, $X$ is definable from $Y$ if and only $X$ is hyperarithmetical in $Y$. We also obtain some related results and pose some related questions.

8 pages. This paper was written in 2000 but was not published until 2018. The only change since 2000 is that the references have been updated