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Jul 15, 2016 at 6:55 comment added Boaz Tsaban Brilliant solution. It is a very old fact that there are Luzin sets in the Cohen model. (Briefly, every Borel meager set is coded using countably many Cohen reals, and all other Cohen reals avoid it.) Every Luzin set is K-Luzin. Thus, I believe that the existence of K-Luzin sets in the Cohen model should be dated to the beginning of the theory of forcing. (It would be nice if someone can add here a more precise dating/source.)
Jul 2, 2016 at 22:14 history edited Taras Banakh CC BY-SA 3.0
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Jul 2, 2016 at 11:41 vote accept Taras Banakh
Jul 1, 2016 at 18:15 history answered Taras Banakh CC BY-SA 3.0