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Solvability of linear equations within the weak mixing sets Alexander Fish February

We introduce a new class of " random " subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We provide necessary and sufficient conditions of solvability of systems of linear equations within every WM subset of N. We also provide a proof of solvability of partition-regular systems (Rado's systems) within every WM subset of N.