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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On second-category sets
HTML articles powered by AMS MathViewer

by P. Komjáth
Proc. Amer. Math. Soc. 107 (1989), 653-654
DOI: https://doi.org/10.1090/S0002-9939-1989-0976358-7
PDF | Request permission

Abstract:

The existence of a measurable cardinal is equiconsistent to the existence of a second category set not decomposable into the union of uncountable many disjoint second category sets.
References
    D. H. Fremlin, Consequences of Martin’s axiom, Cambridge Univ. Press, 1984.
  • Gerald L. Itzkowitz, Continuous measures, Baire category, and uniform continuity in topological groups, Pacific J. Math. 54 (1974), no. 2, 115–125. MR 372114, DOI 10.2140/pjm.1974.54.115
  • Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
  • Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
  • John C. Morgan II, Baire category from an abstract viewpoint, Fund. Math. 94 (1977), no. 1, 13–23. MR 433416, DOI 10.4064/fm-94-1-59-64
  • K. L. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. (Rozprawy Mat.) 68 (1970), 55. MR 262075
  • Wacław Sierpiński, Hypothèse du continu, Chelsea Publishing Co., New York, N. Y., 1956 (French). 2nd ed. MR 0090558
  • Robert M. Solovay, Real-valued measurable cardinals, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR 0290961
    • S. Ulam, Über gewisse Zerlegungen von Mengen, Fund. Math. 20 (1933), 221-223.
Similar Articles
Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 653-654
  • MSC: Primary 03E15; Secondary 03E55, 04A15, 28A12
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0976358-7
  • MathSciNet review: 976358