Scott complexity of reduced Abelian p-groups
Abstract
Given a reduced Abelian p -group, we give an upper bound on the Scott complexity of the group in terms of its Ulm invariants. For limit ordinals, we show that this upper bound is tight. This gives an explicit sequence of such groups with arbitrarily high Scott complexity below ω 1 . Along the way, we give a largely algebraic characterization of the back-and-forth relations on reduced Abelian p -groups, making progress on an open problem of Ash and Knight's from [4] .
Fields of Study & Subjects
Advanced Topology and Set Theory
Rings
Modules
and Algebras
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Annals of Pure and Applied Logic
- Volume
- 177
- Issue
- 7
- Pages
- 103727–103727
- Publication date
- 28 January 2026
- Language
- EN