Fraenkel-Mostowski set theory represents a tool for managing infinite 
structures in terms of finite objects. In this paper we provide a 
connection between the concept of logical notions invariant under 
permutations introduced by Tarski and Fraenkel-Mostowski set theory. 
More precisely, we prove that some particular sets defined by using the 
axioms of  Fraenkel-Mostowski set theory are logical notions in Tarski's 
sense. We also investigate whether a new and specific Fraenkel-Mostowski 
binding operator is logical in Tarski's sense.