2022/06/12 by Yatir Halevi, Halevi, Yatir, Assaf Hasson +3
Mathematics · Computer Science · Arts and Humanities · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Epistemology, Ethics, and Metaphysics
paper · pdf · doi:10.48550/arxiv.2206.05677
We study infinite groups interpretable in three families of valued fields: V-minimal, power bounded T-convex, and p-adically closed fields. We show that every such group G has unbounded exponent and that if G is dp-minimal then it is abelian-by-finite. Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field K, its residue field k (when infinite), its value group Γ, or K/O, where O is the valuation ring. Our work uses and extends techniques developed in [11] to circumvent elimination of imaginaries.