TY - JOUR
T1 - Subtlety and partition relations
AU - Usuba, Toshimichi
N1 - Funding Information:
The author greatly thanks the kind referees for many useful comments, suggestions, and improvements. This research was supported by JSPS and FWF under the Japan-Austria Research Cooperative Program, and by JSPS KAKENHI Grant Number 15K17587.
Publisher Copyright:
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - We study the subtlety of a cardinal κ and of kΛ. We show that, under a certain large cardinal assumption, it is consistent that kΛ is subtle for some Λ > κ but κ is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of PkΛ can be characterized by a certain partition relation on kΛ. We also study the property of faintness of κ, and the subtlety of kΛ with the strong inclusion.
AB - We study the subtlety of a cardinal κ and of kΛ. We show that, under a certain large cardinal assumption, it is consistent that kΛ is subtle for some Λ > κ but κ is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of PkΛ can be characterized by a certain partition relation on kΛ. We also study the property of faintness of κ, and the subtlety of kΛ with the strong inclusion.
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U2 - 10.1002/malq.201400040
DO - 10.1002/malq.201400040
M3 - Article
AN - SCOPUS:84958868776
VL - 62
SP - 59
EP - 71
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
SN - 0942-5616
IS - 1-2
ER -