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Preprint Number 1656

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1656. Caleb Springer
Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ
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Submission date: 2 October 2019

Abstract:

We produce new examples of totally imaginary infinite extensions of ℚ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for ℚ^{(2)}$. In particular, we use parametrized families of polynomials whose roots are totally real units to apply methods originally developed to prove the undecidability of totally real fields.

Mathematics Subject Classification: 11U05

Keywords and phrases:

Full text arXiv 1910.01239: pdf, ps.


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