  We close with an open question about T* and T#.  Recall Definition 3.11, above, which defines when a sentence A of a truth language L is valid in the ground model M by T* or by T#. We will say that A is valid by T* [alternatively, by T#] iff A is valid in the ground model M by T* [alternatively, by T#] for every ground model M. Our open question is this: What is the complexity of the set of sentences valid by T* [T#]?