The length of infinite time Turing machine computations

We show that the halting times of infinite time Turing machines (considered as ordinals coded by sets of integers) are themselves all capable of being halting outputs of such machines. This gives a clarification of the nature of 'supertasks' or infinite time computations. The proof further yields th at the class of sets coded by outputs of halting computations coincides wit h a level of Godel's constructible hierarchy: namely that of L-lambda where lambda is the supremum of halting times. A number of other open questions are thereby answered.