The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to
construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea …

Constructive mathematics is distinguished from its traditional counterpart, classical
mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”. In …

arXiv:2109.04183v1 [math.LO] 9 Sep 2021 Page 1 arXiv:2109.04183v1 [math.LO] 9 Sep
2021 Families of Sets in Bishop Set Theory Iosif Petrakis Mathematics Institute, Ludwig-Maximilians-Universität …

Bishop's measure theory (BMT), introduced in [Bis67], is an abstraction of the measure
theory of a locally compact metric space X, and the use of an informal notion of a set …

We consider three monads on, the category of topological spaces, which formalize
topological aspects of probability and possibility in categorical terms. The first one is the …

We collect several foundational results regarding the interaction between locally compact
spaces, probability spaces and probability algebras, and commutative $ C^* $-algebras and …

This dissertation studies the logic behind quantum physics, using category theory as the
principal tool and conceptual guide. To do so, principles of quantum mechanics are …

Abstract Following Birkhoff and von Neumann, quantum logic has traditionally been based
on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the …

Stochastic approximation algorithms are iterative procedures which are used to approximate
a target value in an environment where the target is unknown and direct observations are …

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum
mechanics, which meanwhile has been extended by Döring and Isham so as to provide a …