Quantum mechanics over sets

This paper gives a toy model of quantum mechanics over the field 2, where the vectors can be interpreted as subsets of a universe set, and hence the name: “Quantum mechanics over sets.” It gives the “logic” of QM in the old-fashioned sense of the essential logic of a theory pared down to operations on sets (vectors over 2). This includes the simplest logical treatment of the double-slit experiment, Bell’s Theorem, the probability calculus based on Born’s Rule, and much else (all restated in the context of sets).