2025/12/20 by Blaise Boissonneau, Boissonneau, Blaise, Lasse Vogel +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Computability, Logic, AI Algorithms
paper · doi:10.48550/arxiv.2512.18349
We study definable ranks of ordered fields, ordered abelian groups, and linear orders. For an arbitrary linear order Γ, we construct an ordered abelian group G with archimedian spine Γ and an ordered field K with natural value group G such that the definable ranks of K, G and Γ are all isomorphic. This answers a question of Krapp, Kuhlmann, and the second author.