In this paper, we study the problem of Byzantine fault-tolerant distributed set intersection and the importance of redundancy in solving this problem. Specifically, consider a distributed system with n agents, each of which has a local set. There are up to f agents that are Byzantine faulty. The goal is to find the intersection of the sets of the non-faulty agents. We are the first to consider the Byzantine set intersection problem with redundancy, and our problem formulation differs from prior works on related problems in different ways. We derive the Byzantine set intersection problem from the Byzantine optimization problem. We present the definition of 2f-set-redundancy for Byzantine set intersection, derived from 2f-redundancy in Byzantine optimization – a necessary condition for Byzantine optimization to be solvable in server-based systems [11]. We study Byzantine set intersection in decentralized (server-less) systems, presenting the necessary and sufficient condition on the communication graph for the Byzantine set intersection problem to be solvable with 2f-set-redundancy. Finally, we present solvability results for Byzantine optimization in decentralized systems, derived from our findings on Byzantine set intersection. Aside from the theoretical results, we also present two practical algorithms for Byzantine set intersection and optimization.