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math.LO2024
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…
math.LO2024
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…