Countable ordinals and the analytical hierarchy. I.

The following results are proved, using the axiom of Projective Determinacy: (i) For n ⪴ 1, every ∏^1_(2n+1) set of countable ordinals contains a Δ^1_(2n+1) ordinal, (ii) For n ⪴ 1, the set of reals Δ^1_(2n) in an ordinal is equal to the largest countable Σ^1_(2n) set and (iii) Every real is Δ^1_n inside some transitive model of set theory if and only if n ⪴ 4.