Non-deterministic clock system

Nondeterministic Moore machines are given by replacing all uses of probability distributions in the above with powerset.

Given a set $\Omega$, we can form a non-deterministic clock system with state space ${\sum }_{i:\mathbb{N}}{\Omega }^{\mathbb{N}}$, with update given by non-deterministically resampling the $i+1,\dots$ coordinates as before