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Colorful Partitions of Cardinal Numbers

Published online by Cambridge University Press:  20 November 2018

J. Baumgartner ,
P. Erdös ,
F. Galvin  and
J. Larson
J. Baumgartner
Affiliation:
Dartmouth College, Hanover, New Hampshire
P. Erdös
Affiliation:
University of Colorado, Boulder, Colorado
F. Galvin
Affiliation:
University of Kansas, Lawrence, Kansas
J. Larson
Affiliation:
University of Florida, Gainesville, Florida
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Use the two element subsets of κ, denoted by [κ]2, as the edge set for the complete graph on κ points. Write CP(κ, µ, v) if there is an edge coloring R: [κ]2 → µ with µ colors so that for every proper v element set X ⊊ κ, there is a point x ∈ κ ∼ X so that the edges between x and X receive at least the minimum of µ and v colors. Write CP⧣(K, µ, v) if the coloring is oneto- one on the edges between x and elements of X.

Peter W. Harley III [5] introduced CP and proved that for κ ≧ ω, CP(κ+, κ, κ) holds to solve a topological problem, since the fact that CP(ℵ1, ℵ0, ℵ0) holds implies the existence of a symmetrizable space on ℵ1 points in which no point is a Gδ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 524 - 541
Copyright
Copyright © Canadian Mathematical Society 1979

References

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