Concept

Quasi-set theory

Résumé
Quasi-set theory is a formal mathematical theory for dealing with collections of objects, some of which may be indistinguishable from one another. Quasi-set theory is mainly motivated by the assumption that certain objects treated in quantum physics are indistinguishable and don't have individuality. Motivation The American Mathematical Society sponsored a 1974 meeting to evaluate the resolution and consequences of the 23 problems Hilbert proposed in 1900. An outcome of that meeting was a new list of mathematical problems, the first of which, due to Manin (1976, p. 36), questioned whether classical set theory was an adequate paradigm for treating collections of indistinguishable elementary particles in quantum mechanics. He suggested that such collections cannot be sets in the usual sense, and that the study of such collections required a "new language". The use of the term quasi-set follows a suggestion in da Costa's 1980 monograph Ensaio sobre os Fundamentos da Lógica
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