Bounding lemmata for non-deterministic halting times of transfinite Turing machines

We use the methods of descriptive set theory and generalized recursion theory to prove various Bounding Lemmata that contribute to a body of results on halting times of non-deterministic infinite time Turing machine computations. In particular we observe that there is a Uniform Bounding Lemma which states that if any total algorithm halts before the first ordinal admissible in the input x, then there is a recursive ordinal γ by which the algorithm halts on all inputs.