A failure detector is a distributed oracle that provides processes in a distributed system with hints about failures. The notion of a weakest failure detector captures the exact amount of synchrony needed for solving a given distributed computing problem. In this paper, we determine the weakest failure detector for solving k-set agreement among n processes (n > k) using reads and writes in shared memory, regardless of the assumptions on when and where failures might occur. This failure detector

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... is derived directly from the impossibility of wait-free k + 1-process k-set agreement. Our approach can be viewed as an extension of the asynchronous BG-simulation technique to partially synchronous systems.