Subtlety and partition relations

Toshimichi Usuba

doi:10.1002/malq.201400040

Subtlety and partition relations

Research output: Contribution to journal › Article › peer-review

Abstract

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 P^kΛ 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.

Original language	English
Pages (from-to)	59-71
Number of pages	13
Journal	Mathematical Logic Quarterly
Volume	62
Issue number	1-2
DOIs	https://doi.org/10.1002/malq.201400040
Publication status	Published - 2016 Feb 1
Externally published	Yes

ASJC Scopus subject areas

Logic

Access to Document

10.1002/malq.201400040

Fingerprint Dive into the research topics of 'Subtlety and partition relations'. Together they form a unique fingerprint.

Cite this

@article{63e47bdd79354f08ac8c216ea2aec766,

title = "Subtlety and partition relations",

abstract = "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.",

author = "Toshimichi Usuba",

year = "2016",

month = feb,

day = "1",

doi = "10.1002/malq.201400040",

language = "English",

volume = "62",

pages = "59--71",

journal = "Mathematical Logic Quarterly",

issn = "0942-5616",

publisher = "Wiley-VCH Verlag",

number = "1-2",

}

TY - JOUR

T1 - Subtlety and partition relations

AU - Usuba, Toshimichi

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.

UR - http://www.scopus.com/inward/record.url?scp=84958868776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958868776&partnerID=8YFLogxK

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 -

Subtlety and partition relations

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this