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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_…