Perfect sets of random reals |
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Authors: | Jörg Brendle Haim Judah |
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Affiliation: | (1) Abraham Fraenkel Center for Mathematical Logic Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel |
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Abstract: | We show that the existence of a perfect set of random reals over a modelM ofZFC does not imply the existence of a dominating real overM, thus answering a well-known open question (see [BJ 1] and [JS 2]). We also prove that (the product of two copies of the random algebra) neither adds a dominating real nor adds a perfect set of random reals (this answers a question that A. Miller asked during the logic year at MSRI). The first author would like to thank the MINERVA-foundation for supporting him. The second author would like to thank the Basic Research Foundation (the Israel Academy of Sciences and Humanities) for supporting him. |
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