  Infinite time Turing machines with only one tape are in many respects fully
as powerful as their multi-tape cousins. In particular, the two models of
machine give rise to the same class of decidable sets, the same degree
structure and, at least for functions f:R-->N, the same class of computable
functions. Nevertheless, there are infinite time computable functions f:R-->R
that are not one-tape computable, and so the two models of supertask
computation are not equivalent. Surprisingly, the class of one-tape computable
functions is not closed under composition; but closing it under composition
yields the full class of all infinite time computable functions. Finally, every
ordinal which is clockable by an infinite time Turing machine is clockable by a
one-tape machine, except certain isolated ordinals that end gaps in the
clockable ordinals.
