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

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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.

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

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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.",

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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.

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ER -

A partition relation for triples using a model of Todorčević

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