# Sh:582

• Gitik, M., & Shelah, S. (2001). More on real-valued measurable cardinals and forcing with ideals. Israel J. Math., 124, 221–242.
• Abstract:
(1) It is shown that if c is real-valued measurable then the Maharam type of (c, {\mathcal 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|\geq\kappa cannot be isomorphic to Random\timesCohen or Cohen\timesRandom. 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.

• published version (22p)
Bib entry
@article{Sh:582,
author = {Gitik, Moti and Shelah, Saharon},
title = {{More on real-valued measurable cardinals and forcing with ideals}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {124},
year = {2001},
pages = {221--242},
issn = {0021-2172},
mrnumber = {1856516},
mrclass = {03E55 (03E35)},
doi = {10.1007/BF02772619},
note = {\href{https://arxiv.org/abs/math/9507208}{arXiv: math/9507208}},
arxiv_number = {math/9507208}
}