TY - JOUR
T1 - Clubs on quasi measurable cardinals
AU - Kumar, Ashutosh
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2018/4
Y1 - 2018/4
N2 - We construct a model satisfying κ<2ℵ0+♣κ+“κ“κ is quasi measurable”. Here, we call κ quasi measurable if there is an ℵ1-saturated κ-additive ideal I on κ. We also show that, in this model, forcing with ℘(κ)\I adds one but not κ Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some ℵ1-saturated κ-additive ideal I on κ, forcing with ℘(κ)\I adds one but not κ random reals.
AB - We construct a model satisfying κ<2ℵ0+♣κ+“κ“κ is quasi measurable”. Here, we call κ quasi measurable if there is an ℵ1-saturated κ-additive ideal I on κ. We also show that, in this model, forcing with ℘(κ)\I adds one but not κ Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some ℵ1-saturated κ-additive ideal I on κ, forcing with ℘(κ)\I adds one but not κ random reals.
UR - http://www.scopus.com/inward/record.url?scp=85046272808&partnerID=8YFLogxK
U2 - 10.1002/malq.201600003
DO - 10.1002/malq.201600003
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AN - SCOPUS:85046272808
SN - 0942-5616
VL - 64
SP - 44
EP - 48
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 1-2
ER -