# Sh:582

- Gitik, M., & Shelah, S. (2001).
*More on real-valued measurable cardinals and forcing with ideals*. Israel J. Math.,**124**, 221–242. arXiv: math/9507208 DOI: 10.1007/BF02772619 MR: 1856516 -
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.

- Version 2000-10-04_10 (24p) 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} }