Modal logic via group homomorphisms defines cyclic subgroup membership, cyclicity, torsion, and finite generation; the homomorphic modal theory of finitely presented groups is computably isomorphic to true arithmetic.
The modal logic of abelian groups
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Modal group theory interprets true arithmetic and establishes that the propositional modal validities of groups under embeddings are exactly S4.2.
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Modal group theory: homomorphisms
Modal logic via group homomorphisms defines cyclic subgroup membership, cyclicity, torsion, and finite generation; the homomorphic modal theory of finitely presented groups is computably isomorphic to true arithmetic.
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Modal group theory
Modal group theory interprets true arithmetic and establishes that the propositional modal validities of groups under embeddings are exactly S4.2.