  The proof of this theorem relies on the fact that a theory can be non-trivially deterministic without being computable. There is an arithmetically definable function which governs the evolution of the system over time (in Humphrey’s construction, the instantaneous state of the system is an arithmetically definable function of the time, which ensures that any two models agreeing at one time will agree at all times, guaranteeing determinism). But the function is not effectively computable, so no algorithm can produce the sequence of  states that this system goes  through.[26]  The physical significance of such uncomputable functions is not clear (though see Pour-El and Richards 1983), but the possibility of a deterministic physics which features such equations of motion is enough to undermine a close connection between randomness and indeterminism. This shows that claim (ii) above is false.