Set-theoretical models for quantum systems

Costa Da Costa

Décio Krause

pp. 171-181

in: Maria L. Dalla Chiara, Roberto Giuntini, Federico Laudisa (eds), Language, quantum, music, Berlin, Springer, 1999

Abstract

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