Geodesic
Colorful Partitions of Cardinal Numbers
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 524-541

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Baumgartner, J.; Erdös, P.; Galvin, F.; Larson, J. Colorful Partitions of Cardinal Numbers. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 524-541. doi: 10.4153/CJM-1979-056-4
@article{10_4153_CJM_1979_056_4,
     author = {Baumgartner, J. and Erd\"os, P. and Galvin, F. and Larson, J.},
     title = {Colorful {Partitions} of {Cardinal} {Numbers}},
     journal = {Canadian journal of mathematics},
     pages = {524--541},
     year = {1979},
     volume = {31},
     number = {3},
     doi = {10.4153/CJM-1979-056-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-056-4/}
}
TY  - JOUR
AU  - Baumgartner, J.
AU  - Erdös, P.
AU  - Galvin, F.
AU  - Larson, J.
TI  - Colorful Partitions of Cardinal Numbers
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 524
EP  - 541
VL  - 31
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-056-4/
DO  - 10.4153/CJM-1979-056-4
ID  - 10_4153_CJM_1979_056_4
ER  - 
%0 Journal Article
%A Baumgartner, J.
%A Erdös, P.
%A Galvin, F.
%A Larson, J.
%T Colorful Partitions of Cardinal Numbers
%J Canadian journal of mathematics
%D 1979
%P 524-541
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-056-4/
%R 10.4153/CJM-1979-056-4
%F 10_4153_CJM_1979_056_4

[1] 1. Baumgartner, J., Almost-dis joint sets, the dense set problem and the partition calculus, Annals Math. Logi. 10 (1976), 401–439. Google Scholar

[2] 2. Ben-David, S., On Shelah's compactness of cardinals, preprint. Google Scholar

[3] 3. Erdos, P., Gillman, L. and Henricksen, M., An isomorphism theorem for real closed fields, Annals of Math. 61 (1955), 542–554. Google Scholar

[4] 4. Erdôs, P., Hajnal, A. and Milner, E. C., On the complete subgraphs of graphs defined by systems of sets, Acta Math. Acad. Sci. Hungarica 17, (1966), 159–229. Google Scholar

[5] 5. Harley III, P. W. and Stephenson, R. M., Jr., Symmetrizable and related spaces, Trans. Amer. Math. Soc. 219 (1976), 89–111. Google Scholar

[6] 6. Milner, E. C., Transversals of disjoint sets, J. London Math. Soc. 43 (1968), 495–500. Google Scholar

[7] 7. Prikry, K., private communication. Google Scholar

[8] 8. Trotter, W., Jr., private communication. Google Scholar

Cité par Sources :