Undecidability, unit groups, and some totally imaginary infinite\n extensions of \ℚ

2019/10/02 by Caleb Springer, Springer, Caleb
Mathematics · #11U05 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.01239

openalex publication_date 2019/10/02 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We produce new examples of totally imaginary infinite extensions of\n\ℚ which have undecidable first-order theory by generalizing the\nmethods used by Martinez-Ranero, Utreras and Videla for \ℚ⁽²⁾. In\nparticular, we use parametrized families of polynomials whose roots are totally\nreal units to apply methods originally developed to prove the undecidability of\ntotally real fields. This proves the undecidability of \ℚ^(d)_ab\nfor all d \≥ 2.\n

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