Andrei Alexandru, Gabriel Ciobanu : On Logical Notions in the Fraenkel-Mostowski Cumulative Universe p. 113-125


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.