Note on a Differential Algebra Bound
Abstract
In a recent article, Freitag, Moosa, and the author showed that in differentially closed fields of characteristic zero, if two types are nonorthogonal, then their n+3 and m+3 Morley powers are not weakly orthogonal, where n and m are their respective Lascar ranks. In this short note, we prove that the bound is tight: There are such types with weakly orthogonal n+2 and m+2 Morley powers. The types in question were constructed by Freitag and Moosa as examples of types with degree of nonminimality 2. As interesting as our result are our methods: We rely mostly on Galois theory and some descent argument for types, combined with the failure of the inverse Galois problem over constant parameters.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Notre Dame Journal of Formal Logic
- Publisher
- Duke University Press
- Volume
- 67
- Issue
- 3
- Pages
- 425–433
- Publication date
- 13 July 2026
- Language
- EN