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Permutation-Invariance and Logicality: A Finite Support Perspective
Andrei Alexandru and Gabriel Ciobanu
The purpose of this work is to explore the connection between Tarski’s notion of logical invariance under permutations and the universe of finitely supported sets, both in the classical Fraenkel-Mostowski axiomatic setting and in recent approaches involving invariant sets. We demonstrate that such finitely supported entities naturally qualify as logical notions in Tarski’s sense, thereby illustrating the structural harmony between symmetry principles in logic and set theory.
Keywords: Fraenkel-Mostowski set theory, Tarski logicality, finitely supported sets, invariant sets