Abstract
For an ordinal \alpha, an \alpha-ITRM is a machine model of transfinite computability that operates on finitely many registers, each of which can contain an ordinal \rho<\alpha; they were introduced by Koepke in \cite{KM}.
In \cite{alpha itrms}, it was shown that the \alpha-ITRM-computable subsets of \alpha are exactly those in a level L_{\beta(\alpha)} of the constructible hierarchy. It was conjectured in \cite{alpha itrms} that \beta(\alpha) is the first limit of admissible ordinals above \alpha. Here, we show that this is false; in particular, even the computational strength of \omega^{\omega}-ITRMs goes far beyond \omega_{\omega}^{\text{CK}}.