Definable Elements of Definable Borel Sets


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We prove that it is true in Sacks, Cohen, and Solovay generic extensions that any ordinal definable Borel set of reals necessarily contains an ordinal definable element. This result has previously been known only for countable sets.

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V. Kanovei

Institute for Information Transmission Problems of Russian Academy of Sciences

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Email: kanovei@iitp.ru
俄罗斯联邦, Moscow, 127051

V. Lyubetsky

Institute for Information Transmission Problems of Russian Academy of Sciences

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Email: lyubetsk@iitp.ru
俄罗斯联邦, Moscow, 127051

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