Modal group theory
逻辑
2026-05-15 v1 群论
摘要
I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton's lemma, I demonstrate that the modal language of groups is more expressive than the first-order language of groups. I interpret the theory of true arithmetic in modal group theory, and show that, as sets of Goedel numbers, it is computably isomorphic to the modal theory of finitely presented groups. I answer an open question of Berger, Block, and Loewe by showing that the formulaic propositional modal validities of groups under embeddings are precisely S4.2. I also analyze sentential validities and worlds validating S5.
引用
@article{arxiv.2605.14197,
title = {Modal group theory},
author = {Wojciech Aleksander Wołoszyn},
journal= {arXiv preprint arXiv:2605.14197},
year = {2026}
}