Undecidability of $\mathbb Q^{(2)}$
Logic
2020-11-03 v1 Number Theory
Abstract
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.
Cite
@article{arxiv.1809.04670,
title = {Undecidability of $\mathbb Q^{(2)}$},
author = {Carlos Martinez-Ranero and Javier Utreras and Carlos R. Videla},
journal= {arXiv preprint arXiv:1809.04670},
year = {2020}
}
Related papers
View all related →
Number Theory · Mathematics
Undecidability, unit groups, and some totally imaginary infinite extensions of $\mathbb{Q}$
Caleb Springer
2020-06-02
Logic · Mathematics
On a question of Abraham Robinson's
Jochen Koenigsmann
2013-11-07
Number Theory · Mathematics
Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields
Alexandra Shlapentokh
2007-05-23
Logic · Mathematics
Undecidability of representability for lattice-ordered semigroups and ordered complemented semigroups
Murray Neuzerling
2015-03-17
Logic · Mathematics
Undecidability of infinite towers of Kummer extensions of $\mathbb{F}_p(t)$
Carlos Martinez-Ranero, Javier Utreras
2024-10-31
Number Theory · Mathematics
Decidability of extensions of Presburger arithmetic by generalised polynomials
Jakub Konieczny
2025-10-08
Logic · Mathematics
Theorems of Tarski's Undefinability and Godel's Second Incompleteness-Computationally
Saeed Salehi
2019-11-12
Number Theory · Mathematics
Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of $\mathbb{Q}_2$
Drew Duncan
2022-12-16
Logic · Mathematics
An undecidability result for the asymptotic theory of $p$-adic fields
Konstantinos Kartas
2022-11-14
Logic in Computer Science · Computer Science
Decidability in the logic of subsequences and supersequences
Prateek Karandikar, Philippe Schnoebelen
2016-07-07
Logic in Computer Science · Computer Science
The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable
Matthias Horbach, Marco Voigt, Christoph Weidenbach
2017-03-06
Logic · Mathematics
An undecidable extension of Morley's theorem on the number of countable models
Christopher J. Eagle, Clovis Hamel, Sandra Müller, Franklin D. Tall
2023-07-06
Algebraic Geometry · Mathematics
Incompressibility of orthogonal grassmannians
Nikita A. Karpenko
2011-10-12
Logic · Mathematics
Remarks on undecidability of indecomposable polynomial rings
Marco Barone, Nicolás Caro-Montoya, Eudes Naziazeno
2023-09-28
Logic · Mathematics
The decision problem for normed spaces over any class of ordered fields
Rob Arthan
2011-05-03
Logic · Mathematics
A dichotomy in classifying quantifiers for finite models
Mor Doron, Saharon Shelah
2007-05-23
Logic · Mathematics
The monadic theory of order
Saharon Shelah
2023-05-02
Representation Theory · Mathematics
Quotient bifinite extensions and the finitistic dimension conjecture
John William MacQuarrie, Fernando dos Reis Naves
2023-06-06
Logic in Computer Science · Computer Science
Conservative Extensions in Guarded and Two-Variable Fragments
Jean Christoph Jung, Carsten Lutz, Mauricio Martel, Thomas Schneider +1
2017-05-30
Logic · Mathematics
Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator
Juvenal Murwanashyaka
2021-11-02
Logic · Mathematics
Most simple extensions of $\mathsf{FL_e}$ are undecidable
Nikolaos Galatos, Gavin St. John
2023-10-04
Number Theory · Mathematics
$2$-superirreducibility of univariate polynomials over $\mathbb{Q}$ and $\mathbb{Z}$
Lara Du
2025-06-18
Logic in Computer Science · Computer Science
The MSO+U theory of (N, <) is undecidable
Mikołaj Bojańczyk, Paweł Parys, Szymon Toruńczyk
2015-02-18
chao-dyn · Physics
Undecidability everywhere?
Karl Svozil
2008-02-03
Number Theory · Mathematics
A non-solvable Galois extension of $\Q$ ramified at 2 only
Lassina Dembele, with a supplement by Jean-Pierre Serre
2008-11-27