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.
Key Words: Fraenkel-Mostowski set theory,
Tarski logicality, invariance, nominal sets, invariant sets.
2010 Mathematics Subject Classification:
Primary 00A30, Secondary 03E30.