7 citations · 7 across the 4 of their papers we have counts for
4 papers
Undecidability of infinite towers of Kummer extensions of
Carlos Martinez-Ranero, Javier Utreras
We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combine…
Undecidability of infinite algebraic extensions of
Carlos Martinez-Ranero, Dubraska Salcedo, Javier Utreras
Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions…
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…
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.