A partition relation for triples using a model of Todorčević

E. C. Milner; K. Prikry

doi:10.1016/0012-365X(91)90336-Z

A partition relation for triples using a model of Todorčević

E. C. Milner
, K. Prikry

School of Mathematics

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

6 Scopus citations

Abstract

Todorčević has shown that there is a ccc extension M in which MA_ω1 + 2^ω = ω₂ holds and also in which the partition relation ω_i → (ω₁,α)² holds for every denumerable ordinal α. We show that the partition relation for triples ω₁ → (ω2 + 1, 4)³ holds in the model M, and hence by absoluteness this is a theorem in ZFC.

Original language	English (US)
Pages (from-to)	183-191
Number of pages	9
Journal	Discrete Mathematics
Volume	95
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(91)90336-Z
State	Published - Dec 3 1991

Bibliographical note

Funding Information:
NSERC Grant No. A5198 and NSF Grant MCS 830361.

Publisher link

10.1016/0012-365X(91)90336-Z

Find It

Find It at U of M Libraries

Cite this

@article{14dd5512e375482ca7acd2ff3b3e93a0,

title = "A partition relation for triples using a model of Todor{\v c}evi{\'c}",

abstract = "Todor{\v c}evi{\'c} has shown that there is a ccc extension M in which MAω1 + 2ω = ω2 holds and also in which the partition relation ωi → (ω1,α)2 holds for every denumerable ordinal α. We show that the partition relation for triples ω1 → (ω2 + 1, 4)3 holds in the model M, and hence by absoluteness this is a theorem in ZFC.",

author = "Milner, \{E. C.\} and K. Prikry",

note = "Funding Information: NSERC Grant No. A5198 and NSF Grant MCS 830361.",

year = "1991",

month = dec,

day = "3",

doi = "10.1016/0012-365X(91)90336-Z",

language = "English (US)",

volume = "95",

pages = "183--191",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - A partition relation for triples using a model of Todorčević

AU - Milner, E. C.

AU - Prikry, K.

N1 - Funding Information: NSERC Grant No. A5198 and NSF Grant MCS 830361.

PY - 1991/12/3

Y1 - 1991/12/3

N2 - Todorčević has shown that there is a ccc extension M in which MAω1 + 2ω = ω2 holds and also in which the partition relation ωi → (ω1,α)2 holds for every denumerable ordinal α. We show that the partition relation for triples ω1 → (ω2 + 1, 4)3 holds in the model M, and hence by absoluteness this is a theorem in ZFC.

AB - Todorčević has shown that there is a ccc extension M in which MAω1 + 2ω = ω2 holds and also in which the partition relation ωi → (ω1,α)2 holds for every denumerable ordinal α. We show that the partition relation for triples ω1 → (ω2 + 1, 4)3 holds in the model M, and hence by absoluteness this is a theorem in ZFC.

UR - https://www.scopus.com/pages/publications/38149144670

UR - https://www.scopus.com/pages/publications/38149144670#tab=citedBy

U2 - 10.1016/0012-365X(91)90336-Z

DO - 10.1016/0012-365X(91)90336-Z

M3 - Article

AN - SCOPUS:38149144670

SN - 0012-365X

VL - 95

SP - 183

EP - 191

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

A partition relation for triples using a model of Todorčević

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this