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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 properties for infinite cardinals. I
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by E. M. Kleinberg PDF
Proc. Amer. Math. Soc. 30 (1971), 371-374 Request permission

Abstract:

Partition properties are perhaps the most fruitful of the various methods for defining and discussing large cardinals in set theory. In this paper we weaken in a natural way the most well known of these partition properties and examine the extent to which the cardinals defined remain “large."
References
  • P. Erdős and A. Hajnal, On the structure of set-mappings, Acta Math. Acad. Sci. Hungar. 9 (1958), 111–131. MR 95124, DOI 10.1007/BF02023868
  • —, Some remarks concerning our paperOn the structure of set mappings,” Acta Math. Acad. Sci. Hungar. 9 (1958), 223-226. E. M. Kleinberg, Somewhat homogeneous sets. I, Notices Amer. Math. Soc. 16 (1969), 840. Abstract #69T-E49. —, Somewhat homogeneous sets. II, Notices Amer. Math. Soc. 16 (1969), 1088. Abstract #69T-E89. —, Somewhat homogeneous sets. III, Notices Amer. Math. Soc. 17 (1970), 296. Abstract #70T-E9. —, Strong partition properties for infinite cardinals, Doctoral Dissertation, Rockefeller University, New York, 1969. J. Silver, Some applications of model theory in set theory, Doctoral Dissertation, University of California, Berkeley, Calif., 1966.
  • Robert M. Solovay, A nonconstructible $\Delta _3^1$ set of integers, Trans. Amer. Math. Soc. 127 (1967), 50–75. MR 211873, DOI 10.1090/S0002-9947-1967-0211873-5
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 30 (1971), 371-374
  • MSC: Primary 04.60; Secondary 02.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0281626-7
  • MathSciNet review: 0281626