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I tried the following:
layer.Where = where;
Map.Extent = layer.FullExtent;
layer.Update();
I tried the following:
layer.Where = where;
Map.Extent = layer.FullExtent;
layer.Update();
You set the Map.Extent too early.
The FullExtent of the layer is updated only after the layer itself has been updated.
So it should work by setting the Map.Extent in an Layer.UpdateCompleted handler.