# A Note on Clockability for Ordinal Turing Machines

## TL;DR

This paper investigates clockability in Ordinal Turing Machines, revealing that admissible ordinals can be clocked, while certain others cannot, and characterizing gaps in clockable ordinals.

## Contribution

It provides new insights into the properties of clockable ordinals for OTMs, contrasting with Infinite Time Turing Machines, and characterizes the structure of clockable ordinal gaps.

## Key findings

- Admissible ordinals can be OTM-clockable.
- $oldsymbol{
m extit{ extSigma}_2}$-admissible ordinals are never OTM-clockable.
- Gaps in OTM-clockable ordinals are initiated by admissible limits of admissible ordinals.

## Abstract

We study clockability for Ordinal Turing Machines (OTMs). In particular, we show that, in contrast to the situation for ITTMs, admissible ordinals can be OTM-clockable, that $\Sigma_{2}$-admissible ordinals are never OTM-clockable and that gaps in the OTM-clockable ordinals are always started by admissible limits of admissible ordinals.