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Quasi-set theory is a first-order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called “indistinguishability” is an extension of identity in the sense that if x is identical to y then x and y are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides us with a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals. This is the first paper of a series that will be dedicated to the philosophical and physical implications of our main mathematical result presented here.
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* Permanent address: Departamento de Matemática, Universidade Federal do Paraná, C. P. 019081, Curitiba, PR, 81531-990, Brazil.
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Sant'Anna*, A. Labels for Non-Individuals?. Found Phys Lett 18, 519–533 (2005). https://doi.org/10.1007/s10702-005-1126-3
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DOI: https://doi.org/10.1007/s10702-005-1126-3