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Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15153 Caleb Springer
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15153 Caleb Springer
Abstract:We produce new examples of totally imaginary infinite extensions of 
which have undecidable first-order theory by generalizing the methods used by Martínez-Ranero, Utreras, and Videla for 
. 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. This proves the undecidability of 
for all 
.
中文翻译：
dec的不可确定性，单位组和一些完全虚构的无限扩展
摘要：通过归纳Martínez-Ranero，Utreras和Videla用于的方法，我们产生了具有完全不确定的一阶理论的完全虚拟无限扩展的新示例。特别是，我们使用参数化的多项式族，其根为完全实数单位，以应用最初开发的方法来证明完全实数字段的不确定性。这证明了所有人的不确定性。
更新日期：2020-09-02
which have undecidable first-order theory by generalizing the methods used by Martínez-Ranero, Utreras, and Videla for . 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. This proves the undecidability of for all . 中文翻译：
dec的不可确定性，单位组和一些完全虚构的无限扩展
摘要：通过归纳Martínez-Ranero，Utreras和Videla用于的方法，我们产生了具有完全不确定的一阶理论的完全虚拟无限扩展的新示例。特别是，我们使用参数化的多项式族，其根为完全实数单位，以应用最初开发的方法来证明完全实数字段的不确定性。这证明了所有人的不确定性。
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