TY - JOUR
T1 - New combinatorial principle on singular cardinals and normal ideals
AU - Usuba, Toshimichi
N1 - Funding Information:
This research was supported by JSPS KAKENHI grant Nos. 15K17587 and 15K04984.
Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2018/11
Y1 - 2018/11
N2 - We introduce a new combinatorial principle on singular cardinals. This principle allows us to take a kind of a diagonal intersection of more than λ many measure one sets of certain normal ideals over ℘(λ). Under the principle, we give various characterizations of the saturation property of normal ideals over ℘(λ). We also consider Chang's type transfer properties under the principle, and, when λ is Jónsson, we prove that every normal ideal over ℘(λ) with {x ⊆ λ : |x| = λ} measure one cannot have strong properties.
AB - We introduce a new combinatorial principle on singular cardinals. This principle allows us to take a kind of a diagonal intersection of more than λ many measure one sets of certain normal ideals over ℘(λ). Under the principle, we give various characterizations of the saturation property of normal ideals over ℘(λ). We also consider Chang's type transfer properties under the principle, and, when λ is Jónsson, we prove that every normal ideal over ℘(λ) with {x ⊆ λ : |x| = λ} measure one cannot have strong properties.
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U2 - 10.1002/malq.201700024
DO - 10.1002/malq.201700024
M3 - Article
AN - SCOPUS:85055553537
VL - 64
SP - 395
EP - 408
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
SN - 0942-5616
IS - 4-5
ER -