Modal group theory

Wojciech Aleksander Wołoszyn

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arXiv · 2605.14197

Modal group theory

Wojciech Aleksander Wołoszyn

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Abstract

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.

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BibTeX RIS

Wojciech Aleksander Wołoszyn. 2026-05-13. Modal group theory. https://arxiv.org/abs/2605.14197

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