### More on real-valued measurable cardinals and forcing with ideals

by Gitik and Shelah. [GiSh:582]

Israel J Math, 2001

(1) It is shown that if c is real-valued measurable then the
Maharam type of (c, P (c), sigma) is 2^c . This answers a
question of D. Fremlin.
(2) A different construction of a model with a real-valued
measurable cardinal is given from that of R. Solovay. This answers a
question of D. Fremlin.
(3) The forcing with a kappa-complete ideal over a set X,
|X| >= kappa cannot be isomorphic to Random x Cohen or
Cohen x Random. The result for X= kappa was proved in
[GiSh:357] but as was pointed out to us by M. Burke the application
of it in [GiSh:412] requires dealing with any X .

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