# Sh:1063

- Kumar, A., & Shelah, S. (2018).
*Clubs on quasi measurable cardinals*. MLQ Math. Log. Q.,**64**(1-2), 44–48. DOI: 10.1002/malq.201600003 MR: 3803065 -
Abstract:

We construct a model satisfying \kappa < 2^{\aleph_0} + \clubsuit_{\kappa} +\kappa is quasi measurable. Here, we call \kappa quasi measurable if there is an \aleph_1-saturated \kappa-additive ideal \mathcal{I} over \kappa. We also show that, in this model, forcing with \mathcal{P}(\kappa)/ \mathcal{I} adds one but not \kappa Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some \aleph_{\mathcal{1}}-saturated \kappa-additive ideal \mathcal{I} over \kappa, forcing with P(\kappa) /I adds one but not \kappa random reals. - published version (5p)

Bib entry

@article{Sh:1063, author = {Kumar, Ashutosh and Shelah, Saharon}, title = {{Clubs on quasi measurable cardinals}}, journal = {MLQ Math. Log. Q.}, fjournal = {MLQ. Mathematical Logic Quarterly}, volume = {64}, number = {1-2}, year = {2018}, pages = {44--48}, issn = {0942-5616}, mrnumber = {3803065}, mrclass = {03E35 (03E40 03E55)}, doi = {10.1002/malq.201600003} }