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Definable hereditary families in the projective hierarchy

R. Barua, V. Srivatsa (1992)

Fundamenta Mathematicae

We show that if ℱ is a hereditary family of subsets of ω ω satisfying certain definable conditions, then the Δ 1 1 reals are precisely the reals α such that β : α Δ 1 1 ( β ) . This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the Q 2 n + 1 -encodable reals is also shown.

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