  Schindler recently addressed two versions of the question P $\stackrel{?}{=}$
NP for Turing machines running in transfinite ordinal time. These versions
differ in their definition of input length. The corresponding complexity
classes are labelled P, NP and ${\rm P}^+,{\rm NP}^+$. Schindler showed that P
$\neq$ NP and ${\rm P}^+ \neq {\rm NP}^+$. We show that P $=$ NP $\cap$ co-NP
and NP $\neq$ co-NP, whereas ${\rm P}^+ \subset$ NP $\cap$ co-NP and ${\rm
NP}^+ \neq $ co-NP$^+$.
