Abstract
In this paper we prove two (rather unrelated) theorems about projective sets. The first one asserts that subsets of ℵ_1 which are ∑^1_2 in the codes are constructible; thus it extends the familiar theorem of Shoenfield that ∑^1_2 subsets of ω are constructible. The second is concerned with largest countable ∑^1_(2n) sets and establishes their existence under the hypothesis of Projective Determinacy and the assumption that there exist only countably many ordinal definable reals.
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