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  1. A Groszek‐Laver pair of undistinguishable ‐classes.Mohammad Golshani, Vladimir Kanovei & Vassily Lyubetsky - 2017 - Mathematical Logic Quarterly 63 (1-2):19-31.
    A generic extension of the constructible universe by reals is defined, in which the union of ‐classes of x and y is a lightface set, but neither of these two ‐classes is separately ordinal‐definable.
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  • Countable OD sets of reals belong to the ground model.Vladimir Kanovei & Vassily Lyubetsky - 2018 - Archive for Mathematical Logic 57 (3-4):285-298.
    It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of \ elements.
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