paper

The theory of the Ziegler degrees

arXiv:2607.02870

Abstract

The Ziegler degrees were introduced to characterize definability in group theory. In [JLSta], the authors show that the first order-theory of the Ziegler degrees (as a partial order) is undecidable. We improve this result, showing that the theory of the Ziegler degrees is bi-interpretable with true second-order arithmetic.

13 pages; comments welcome!