Axioms for collections of indistinguishable objects

Décio Krause

Abstract


The search for axioms like those of set theories for dealing with collections of indistinguishable elementary particles was posed by Yu. Manin, in 1974, as one of the important problems of present day researches on the foundations of mathematics. In this paper we presented a quasi-set theory which stands for a mathematical framework for dealing with collections of indistinguishable objects, whose 'intended interpretation' is precisely the behaviour of elementary particles as described by non-relativistic quantum mechanics. A sketch of the proof that this theory and ZFC are equiconsistent is also presented and the relationship with the case of quantum particles is mentioned throughout the paper.

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