## A Bridge Between Q-Worlds

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2021
Döring, Andreas
Ozawa, Masanao
Journal article
Published
##### Published in
The Review of Symbolic Logic ; 14 (2021), 2. - pp. 447-486. - Cambridge University Press. - ISSN 1755-0203. - eISSN 1755-0211
##### Abstract
Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding quantum mechanics by reformulating parts of the theory inside of non-classical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, Q-worlds'. Here, we provide a unifying framework that allows us to (i) better understand the relationship between different Q-worlds, and (ii) define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches. Along the way, we develop a novel connection to paraconsistent logic and introduce a new class of structures that have significant implications for recent work on paraconsistent set theory.
100 Philosophy
##### Cite This
ISO 690DÖRING, Andreas, Benjamin EVA, Masanao OZAWA, 2021. A Bridge Between Q-Worlds. In: The Review of Symbolic Logic. Cambridge University Press. 14(2), pp. 447-486. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020319000492
BibTex
@article{Doring2021Bridg-53570,
year={2021},
doi={10.1017/S1755020319000492},
title={A Bridge Between Q-Worlds},
number={2},
volume={14},
issn={1755-0203},
journal={The Review of Symbolic Logic},
pages={447--486},
author={Döring, Andreas and Eva, Benjamin and Ozawa, Masanao}
}

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