In this paper, we show that the non-deterministic choice “+”, which was proposed as a primitive operator in Synchronization Tree Logic (STL for short) can be defined essentially by conjunction and disjunction in the μ-calculus (μM for short). This is obtained by extending the μ-calculus with the non-deterministic choice “+” (denoted by μM+) and then showing that μM+ can be translated into μM. Furthermore, we also prove that STL can be encoded into μM+ and therefore into μM.