Set-theoretical models for quantum systems

da Costa Newton C.A.; Krause Décio

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(1999) Language, quantum, music, Dordrecht, Springer.

Set-theoretical models for quantum systems

Newton C.A. da Costa , Décio Krause

pp. 171-181

The general mathematical framework underlying the usual physical theories is naïve set theory, but it is obvious that every construction can be performed in an axiomatized set theory like Zermelo-Fraenkel or Kelley-Morse. In fact, we could consider the axiomatization of physical theories by means of Suppes' predicates (or Bourbaki's species of structures), which are formulas of set theory, and note that the models of such predicates are also set-theoretical structures [6]. In particular, the usual formulations of quantum mechanics (henceforth, QM) use a fragment of the language of functional analysis; so, they are based on set theory.¹

Publication details

DOI: 10.1007/978-94-017-2043-4_16

Full citation:

da Costa, N. C. , Krause, D. (1999)., Set-theoretical models for quantum systems, in M. L. Dalla Chiara, R. Giuntini & F. Laudisa (eds.), Language, quantum, music, Dordrecht, Springer, pp. 171-181.

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