Perfect sets of random reals
| dc.creator | Brendle, Jörg | |
| dc.creator | Judah, Haim | |
| dc.date | 1992-09-15 | |
| dc.date.accessioned | 2026-07-07T09:14:49Z | |
| dc.date.available | 2026-07-07T09:14:49Z | |
| dc.description | We discuss the relationship between perfect sets of random reals, dominating reals, and the product of two copies of the random algebra B. Recall that B is the algebra of Borel sets of 2^omega modulo the null sets. Also given two models M subseteq N of ZFC, we say that g in omega^omega cap N is a dominating real over M iff forall f in omega^omega cap M there is m in omega such that forall n geq m (g(n) > f(n)); and r in 2^omega cap N is random over M iff r avoids all Borel null sets coded in M iff r is determined by some filter which is B-generic over M. We show that there is a ccc partial order P which adds a perfect set of random reals without adding a dominating real, thus answering a question asked by the second author in joint work with T. Bartoszynski and S. Shelah some time ago. The method of the proof of this result yields also that B times B does not add a dominating real. By a different argument we show that B times B does not add a perfect set of random reals (this answers a question that A. Miller asked during the logic year at MSRI). | |
| dc.identifier | https://arxiv.org/abs/math/9209205 | |
| dc.identifier | http://arxiv.org/abs/math/9209205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152811 | |
| dc.subject | Logic | |
| dc.title | Perfect sets of random reals | |
| dc.type | text |