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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