1 citations · 1 across the 5 of their papers we have counts for
5 papers
Non-Diophantine sets in rings of functions
Natalia Garcia-Fritz, Hector Pasten, Thanases Pheidas
Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contr…
Decidability of the theory of addition and the Frobenius map in rings of rational functions
Dimitra Chompitaki, Manos Kamarianakis, Thanases Pheidas
We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let be a pri…
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…
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…
Division-ample sets and the Diophantine problem for rings of integers
Gunther Cornelissen, Thanases Pheidas, Karim Zahidi
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division…