We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle CD-PB, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than. Any ω-model of must be closed under hyperarithmetic reduction, but is not a theory of hyperarithmetic analysis. We show that whenever is the second-order part of an ω-model of CD-PB, then for every Z M, there is a G M such that G is Δ-generic relative to Z.
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