Admissible ordinals are OTM-clockable, Σ₂-admissible ordinals are never OTM-clockable, and gaps in the OTM-clockable ordinals begin at admissible limits of admissible ordinals.
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A Note on Clockability for Ordinal Turing Machines
Admissible ordinals are OTM-clockable, Σ₂-admissible ordinals are never OTM-clockable, and gaps in the OTM-clockable ordinals begin at admissible limits of admissible ordinals.