A partition relation for pairs on ω ω ω

We consider colorings of the pairs of a family F⊆FIN of topological type ωωk, for k>1; and we find a homogeneous family G⊆F for each coloring. As a consequence, we complete our study of the partition relation ∀l>1,α→(topω2+1)l,m2 identifying ωωω as the smallest ordinal space α1,α→(topω2+1)l,42...

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Bibliographic Details
Published in:Archive for mathematical logic 2018-01, Vol.57 (7), p.727-753
Main Author: Piña, Claribet
Format: Article
Language:English
Subjects:
Coloring
Partitions (mathematics)
Online Access:Get full text
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Summary:We consider colorings of the pairs of a family F⊆FIN of topological type ωωk, for k>1; and we find a homogeneous family G⊆F for each coloring. As a consequence, we complete our study of the partition relation ∀l>1,α→(topω2+1)l,m2 identifying ωωω as the smallest ordinal space α1,α→(topω2+1)l,42.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-017-0604-1