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Undecidability of $ \mathbb{Q}^{(2)}$


Authors: Carlos Martínez-Ranero, Javier Utreras and Carlos R. Videla
Journal: Proc. Amer. Math. Soc. 148 (2020), 961-964
MSC (2010): Primary 11U05; Secondary 03B25, 11R11
DOI: https://doi.org/10.1090/proc/14849
Published electronically: December 6, 2019
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Abstract: It is shown that the compositum $ \mathbb{Q}^{(2)}$ of all degree 2 extensions of $ \mathbb{Q}$ has undecidable theory.


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Carlos Martínez-Ranero
Affiliation: Facultad de Ciencias Físicas y Matemáticas, Departamento de Matemática, Universidad de Concepción, Concepción, Chile
Email: cmartinezr@udec.cl

Javier Utreras
Affiliation: Facultad de Ciencias Físicas y Matemáticas, Departamento de Matemática, Universidad de Concepción, Concepción, Chile
Email: javierutreras@udec.cl

Carlos R. Videla
Affiliation: Department of Mathematics and Computing, Mount Royal University, Calgary, Canada
Email: cvidela@mtroyal.ca

DOI: https://doi.org/10.1090/proc/14849
Received by editor(s): August 30, 2018
Received by editor(s) in revised form: May 17, 2019, and July 1, 2019
Published electronically: December 6, 2019
Additional Notes: The first-named author was supported by Proyecto VRID-Enlace No. 218.015.022-1.0
The second-named author was supported by FONDECYT-Postdoctorado No. 3160301
Part of this work was done while the third author was visiting X. Vidaux in Concepción during May 2018 under Conicyt Project: Fondecyt 1170315
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2019 American Mathematical Society