1 citations · 1 across the 7 of their papers we have counts for
11 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…
Effectivity for existence of rational points is undecidable
Natalia Garcia-Fritz, Hector Pasten, Xavier Vidaux
The analogue of Hilbert's tenth problem over asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as o…
Existential decidability for addition and divisibility in holomorphy subrings of global fields
Carlos Martinez-Ranero, Javier Utreras, Xavier Vidaux
We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of glob…
Optimal bounds for Büchi's problem in modular arithmetic II
Pablo Sáez, Xavier Vidaux, Maxim Vsemirnov
Given a prime and an integer , we show that there exists an integer such that for any quadratic polynomial with coefficients in the ring of integers modulo $…
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…
Hilbert's tenth problem for complex meromorphic functions in several variables
Thanases Pheidas, Xavier Vidaux
We prove an analogue of Hilbert's Tenth Problem for complex meromorphic functions. More precisely, we prove that the set of integers is positive existentially definable in fields o…
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…
Uniform Definability and Undecidability in Classes of Structures
Hector Pasten, Thanases Pheidas, Xavier Vidaux
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for…
A characterization of Büchi's integer sequences of length 3
Pablo Saéz, Xavier Vidaux
We give a new characterization of generalized Büchi sequences (sequences whose sequence of squares has constant second difference , for some fixed integer ) of length 3 ove…
Polynomial parametrizations of length Büchi sequences
Xavier Vidaux
Büchi's problem asks whether there exists a positive integer such that any sequence of at least integers, whose second difference of squares is the constant sequenc…
The analogue of Büchi's problem for function fields
Alexandra Shlapentokh, Xavier Vidaux
Büchi's Squares Problem asks for an integer such that any sequence , whose second difference of squares is the constant sequence (i.e. $x^2_n-2x^2_…