Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

120 a potential subtlety concerning the distinctionholds across the entire multiverse (of mathematical versions of the universe) definedby the specified laws.Our construction of e 0 actually gives a Turing program e0 ∗ that witnesses a moredramatic version of the property just discussed, and it is this program that is the basisfor our claim of a potentially subtle aspect to the distinction of determinism versusnondeterminism. We describe e0 ∗ first more formally and then informally.If in a given universe no output is generated by e0 ∗ with input 0, then by extendingtime one can arrange that any specified finite binary sequence is now the output of e0∗acting on input 1. Otherwise, in the given universe, e0 ∗ computes a finite (positive)integer N 0 from input 0, and for any specified finite binary sequence, by extending timeone can arrange that for some input i