A note on forcing with ideals and Hechler forcing. (English) Zbl 1052.03032
Let \(\kappa\) be an infinite cardinal, \({\mathcal B}\) a Boolean algebra. \({\mathcal B}\) is \(\kappa\)-representable if there is a \(\kappa\)-complete ideal \(I\) on \(\kappa\) such that \({\mathcal B}\cong{\mathcal P}(\kappa)/{\mathcal I}\).
Gitik and Shelah have shown that the Hechler algebra \({\mathcal H}\) (the Boolen algebra of regular open sets of Hechler forcing) is not representable. Here the author gives a simpler proof of this fact using some observation concerning Hechler forcing.
Gitik and Shelah have shown that the Hechler algebra \({\mathcal H}\) (the Boolen algebra of regular open sets of Hechler forcing) is not representable. Here the author gives a simpler proof of this fact using some observation concerning Hechler forcing.
Reviewer: Martin Weese (Potsdam)
MSC:
03E40 | Other aspects of forcing and Boolean-valued models |
06E10 | Chain conditions, complete algebras |