Subtlety and partition relations
We study the subtlety of a cardinal κ and of ℘κλ. We show that, under a certain large cardinal assumption, it is consistent that ℘κλ 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 subtl...
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| Published in | Mathematical logic quarterly Vol. 62; no. 1-2; pp. 59 - 71 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
Blackwell Publishing Ltd
01.02.2016
Wiley Subscription Services, Inc |
| Online Access | Get full text |
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| Summary: | We study the subtlety of a cardinal κ and of ℘κλ. We show that, under a certain large cardinal assumption, it is consistent that ℘κλ 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 ℘κλ can be characterized by a certain partition relation on ℘κλ. We also study the property of faintness of κ, and the subtlety of ℘κλ with the strong inclusion. |
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| Bibliography: | istex:5AD8A8AF55CB4B1F8AE957E8A87EBE2147ED6FF1 ark:/67375/WNG-3ZHFNF6K-L Japan-Austria Research Cooperative Program - No. 15K17587 ArticleID:MALQ201400040 |
| ISSN: | 0942-5616 1521-3870 |
| DOI: | 10.1002/malq.201400040 |