A note on the modal logic of symmetric extensions
Logic
2026-05-08 v1
Abstract
Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular, we define the concept of of choice-switches, and show any independent system of choice-switches is not itself independent from any standard example of an independent system of buttons.
Cite
@article{arxiv.2605.05462,
title = {A note on the modal logic of symmetric extensions},
author = {Hope Duncan},
journal= {arXiv preprint arXiv:2605.05462},
year = {2026}
}
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10 pages