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A Theorem in the Partition Calculus

Published online by Cambridge University Press:  20 November 2018

P. Erdös  and
E. C. Milner
P. Erdös
Affiliation:
University of Calgary, Calgary, Alberta
E. C. Milner
Affiliation:
University of Calgary, Calgary, Alberta
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If S is an ordered set we write tp S to denote the order type of S and |5| for the cardinal of S. We also write [S]k for the set {X:X ⊂ S, |X|=k}. The partition symbol

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Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 501 - 505
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Chang, C. C., A partition theorem for the complete graph on ωω , J. Combinatorial Theory Ser. A, 12(1972), 396-452.Google Scholar
2. Erdös, P. and Rado, R., A partition calculus in set theory, Bull. Amer. Math. Soc. 62(1956), 427-489.Google Scholar
3. Erdös, P. and Rado, R., Partition relations and transitivity domains of binary relations, J. London Math. Soc. 42 (1967), 624-633.Google Scholar
4. Hajnal, A. and Milner, E. C., Some theorems for scattered ordered types, Periodica Matematika Hungaricae (2) 1 (1971), 81-92.Google Scholar
5. Laver, R., On Fraissé's order type conjecture, Ann. of Math. (2) 93 (1971), 89-111.Google Scholar
6. Milner, E. C., Ph.D. Thesis, London, 1962.Google Scholar
7. Milner, E. C., Partition relations for ordinal numbers, Canad. J. Math. 21 (1969), 317-334.Google Scholar
8. Milner, E. C. and Rado, R., The pigeon-hole principle for ordinal numbers, Proc. London Math. Soc. (3) 15(1965), 750-768.Google Scholar
9. Haddad, L. and Sabbagh, G., Sur une extension des nombres de Ramsey aux ordinaux, C.R. Acad. Sci. Paris, 268(1969), 1165-1167.Google Scholar
10. Haddad, L. and Sabbagh, G., Calcul de certains nombres de Ramsey généralisés, C.R. Acad. Sci. Paris, 268 (1969), 1233-1234.Google Scholar
11. Haddad, L. and Sabbagh, G., Nouveaux résultats sur les nombres de Ramsey généralisés, C.R. Acad. Sci. Paris, 268(1969), 1516-1518.Google Scholar