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Abstract: We present recent results about finite jet determination of CR maps of positive codimension from real-analytic CR manifolds into real-algebraic subsets in complex space, or more generally Nash subsets. One instance of such results is the unique jet determination of germs of CR maps from minimal real-analytic CR submanifolds in \(C^N\) into Nash subsets in \(C^{N'}\) of D'Angelo finite type, for arbitrary \(N,N'geq 2\). This is joint work with B. Lamel.