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)

@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}
}