A measure-preserving system is U-mixing if and only if it is disjoint from every U-generated system, and every partially rigid system is a finite extension of some U-generated system.
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Multipliers and Disjointness from Mixing
A measure-preserving system is U-mixing if and only if it is disjoint from every U-generated system, and every partially rigid system is a finite extension of some U-generated system.