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math.LO2025
Borel Complexity of the set of vectors normal for a fixed recurrence sequence
Hajime Kaneko, Bill Mance
In this paper, we consider recurrence sequences () with companion polynomial . For example, the sequence $x_n=ξ_1(4+\sqrt{2})^n+΅
math.LO2025
Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem
Sohail Farhangi, Steve Jackson, Bill Mance
We show that several sets of interest arising from the study of partition regularity and density Ramsey theory of polynomial equations over integral domains are undecidable. In par…