Why aren't valid higher order logic sentences recursively enumerable in full semantics? It's said (proven in some reduction to the Gödel–Rosser theorem?) that second order logic and higher fails to be complete for full semantics; that is there isn't any semi-algorithm for determining if a sentence is valid in full semantics. Yet full semantics I understand is reducible to set theory, and set theory is expressible as a first order theory and so it's theorems are recursively enumerable. 
Why can't we simply translate a higher order logic sentence into first order set theory to test it for validity? Does this not work? Or does this only work for sentences in set theory but not for some sentences in higher order logic that are 'true but unprovable' in full semantics?
Does this mean higher order logic and set theory aren't isomorphic?

The set of valid sentences using just equality in second order logic is a very complex set (The analogous set in first order logic is computable and c.e. if non logical symbols are allowed). Using Tarski's theorem on undefinability of truth, you can show that this set is not even analytical (lightface projective) - This is the analogue of the fact the true arithmetic is not arithmetical.
