7 citations · 7 across the 4 of their papers we have counts for
5 papers
An approach to Julia Robinson numbers through the lattice of subfields
Xavier Vidaux, Carlos R. Videla
By fully describing the lattice of subfields of some towers of number fields built by iterating square roots, we obtain infinitely many fields, each of them either contradicts Juli…
Undecidability of
Carlos Martinez-Ranero, Javier Utreras, Carlos R. Videla
It is shown that the compositum of all degree 2 extensions of has undecidable theory.
Dedekind's criterion for the monogenicity of a number field versus Uchida's and Lüneburg's
Xavier Vidaux, Carlos R. Videla
We compare three different characterizations, due respectively to R. Dedekind, K. Uchida, and H. Lüneburg, of when is the ring of integers of , and app…
Julia Robinson numbers and arithmetical dynamic of quadratic polynomials
Marianela Castillo Fernández, Xavier Vidaux, Carlos R. Videla
For rings of totally real algebraic integers, J. Robinson defined a set which is always or of the form or for some real nu…
Definability and Decidability in Infinite Algebraic Extensions
Alexandra Shlapentokh, Carlos Videla
We use a generalization of a construction by Ziegler to show that for any field and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$…