A Topos Perspective on State-Vector Reduction

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A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all M-sets, where M is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a `neo-realist' interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction.