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Abstract
In a previous work it was shown that it is possible to deal with collections of indistinguishable elementary particles in a set-theoretical framework, by using hidden variables. We propose in the present paper a set-theoretical axiomatics for collections of indiscernibles with no explicit mention to hidden variables. We also show, in this context, the fundamental role of the (micro) state in the process of individuation of classical and quantum particles. Finally, we discuss the importance of the axiom of choice in Zermelo-Fraenkel set theory in the context of quantum distributions of bosons and fermions.
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