Definable maximal discrete sets in forcing extensions
Research output: Contribution to journal › Journal article › Research › peer-review
Let be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing that in the Sacks and Miller extensions there is a Π11 maximal orthogonal family ("mof") of Borel probability measures on Cantor space. A similar result is also obtained for Π11 mad families. By contrast, we show that if there is a Mathias real over L then there are no Σ12 mofs.
Original language | English |
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Journal | Mathematical Research Letters |
Volume | 25 |
Issue number | 5 |
Pages (from-to) | 1591-1612 |
ISSN | 1073-2780 |
DOIs | |
Publication status | Published - 2018 |
Links
- http://arxiv.org/pdf/1510.08781
Submitted manuscript
ID: 184033460