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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weak partition relations
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by Andreas Blass PDF
Proc. Amer. Math. Soc. 35 (1972), 249-253 Request permission

Abstract:

The partition relation ${\aleph _1} \to ({\aleph _1})_{3,2}^2$, which was known to contradict the continuum hypothesis [1], is disproved without this hypothesis.
References
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  • Fred Galvin and Saharon Shelah, Some counterexamples in the partition calculus, J. Combinatorial Theory Ser. A 15 (1973), 167–174. MR 329900, DOI 10.1016/s0097-3165(73)80004-4
  • E. M. Kleinberg, Somewhat homogeneous sets. I, Notices Amer. Math. Soc. 16 (1969), 840. Abstract #69T-E49. G. Kurepa, Ensembles linéaires et une classe de tableaux ramifiés (tableaux ramifiés de M. Aronszajn), Publ. Inst. Math. (Beograd) 6 (1936), 129-160.
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  • F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.
  • Mary Ellen Rudin, Souslin’s conjecture, Amer. Math. Monthly 76 (1969), 1113–1119. MR 270322, DOI 10.2307/2317183
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 249-253
  • MSC: Primary 04A20
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0297576-7
  • MathSciNet review: 0297576