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arXiv · 2607.02870

The theory of the Ziegler degrees

Rodney G. Downey·Steffen Lempp·Isabella Scott
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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.

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Rodney G. Downey, Steffen Lempp, Isabella Scott. 2026-07-03. The theory of the Ziegler degrees. https://arxiv.org/abs/2607.02870

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