Listing the hyperarithmetical functions

Joseph S. Miller, Gian Marco Osso, Isabella Scott

Given a countable Turing ideal $\mathcal{I}\subseteq \ddot{I}{‰}^{\ddot{I}}‰$, we say that $x$ is a list (resp. weak list) of $\mathcal{I}$ if $\mathcal{I}=\{x^{[n]}:n\in \ddot{I}‰\}$ (resp. if $\mathc…