Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is reachability: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that visits a vertex in $T$ at least once (i.e. you want to reach some vertex in $T$). Furthermore, given $k$ reachability objectives, the disjunctive reachability query question asks whether there is a strategy for player 1 to ensure that one of the reachability objectives is satisfied with probability 1. Disjunctive queries do not coincide with disjunctive objectives on MDPs.