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We introduce time and space complexity classes of the P and PSPACE families for
ordinal Turing Machines by Peter Koepke. We establish a number of connections
between these classes internally, and between these classes and the earlier
defined time-complexity classes for infinite time Turing machines as defined by
Joel Hamkins and Andy Lewis. Furthermore, we give a partial negative answer to
the question whether these space complexity classes can somehow be related to
the ITTM degrees defined by Hamkins/Lewis.