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.

arXiv comment8 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