More on real-valued measurable cardinals and forcing with ideals

1995/07/05 by Gitik, Moti, Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/9507208

Abstract

Answering two questions of D. Fremlin [Real-valued measurable cardinals, in Set Theory of the Reals, H. Judah ed. 1993, 151-305 ] we show the following: (1) If c is real-valued measurable then the Maharam type of (c,P(c),sigma) is 2^c. (2) It is consistent to have k real-valued measurable but for every submodel V₁ with k measurable in it there are no k reals which are random over V₁.

Related

• Models of real-valued measurability
• Generalizing random real forcing for inaccessible cardinals
• Regularity Properties on the Generalized Reals
• Prikry-type forcing and the set of possible cofinalities
• Changing measurable into small accessible cardinals